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Loan payment formula 2019-02-24
From Kenneth:

I have a question regarding the loan payment formula shown below.

Calculating the Payment Amount per Period
The formula for calculating the payment amount is shown below.

Simple Amortization Calculation Formula

A = P X r(1 + r)n over (1 + r)n - 1

where

A = payment Amount per period

P = initial Principal (loan amount)
r = interest rate per period

n = total number of payments or periods

Is this formula/calculation a condensed version of a longer calculation? I am curious to know how the (1 +r)n - 1 was developed from the longer calculation. For example, r(1 + r)n may have been (r + rn)n. The n's are exponents.

I thank you for whatever helpful explanation that may be provided.

Kenneth

A geometric series 2018-03-13
From nathi:
a pohutukawa tree is 86 centimetres when it is planted. in the first year after it is planted , the tree grows 42 centimetres in height.Each year the tree grows in height by 95% of the growth of the previous year.
assume that the growth in height of the pohutukawa tree can be modelled by a geometric sequence.
A)find the height of the tree 5 years after it is planted and figure out the maximum height the pohutukawa tree is expected to reach in centimetres. The maximum height part is not answered.

A road trip word problem 2016-04-10
From Marc:
While on a road trip I imagined this random word problem. Suppose I start a trip of 75 miles. My initial speed is 75 miles per hour. After every mile traveled I decrease my speed by one mile per hour. After the first mile I decrease my speed to 74 miles per hour and so on for each subsequent mile traveled. How long will it take to complete the 75 mile journey?
Which term of the series 2+7+12+...is 152? 2016-02-01
From francis:
whice term of the series 2+7+12+...is 152?
The sum of the first 50 terms of an arithmetic progression 2014-07-26
From Joshua:
Hello ...my is Joshua...I'm a grade 11 student...I got a question

Calculate the sum of the first 50 terms of an arithmetic progression: 112:98:84

An infinite geometric series 2013-12-24
The sum of an infinite geometric series is 15 and the sum of their squares is 45. Find the series
A sequence or a series? 2013-09-05
From Rahul:
Whether the following sequence is increasing or decreasing? I even do not kow whether to call it a sequence or not. an = (1/(1+n))+(1/(2+n))+....+(1/(n+n)). I am confused. It looks like a series to me. Please help.
Regards,
Rahul

An arithmetic progression 2012-08-22
From A student:
the 3rd term of an A.PPP is 10 more than the first term while the 5th term is 15 more than the second.find the sum of the 8th and 15th terms if the 7th term is 7 times the first term.
1+2+4+8....= -1 2012-04-02
From Andy:
In this minutephysics video, it's claimed that 1+2+4+8....= -1 Is this true, and if so, how?

A tree growth modelled by a geometric series 2012-02-08
From Steph:
a pohutukawa tree is 86 centimetres when it is planted. in the first year after it is planted , the tree grows 42 centimetres in height.Each year the tree grows in height by 95% of the growth of the previous year. assume that the growth in height of the pohutukawa tree can be modelled by a geometric sequence.
A)find the height of the tree 5 years after it is planted and figure out the maximum height the pohutukawa tree is expected to reach in centimetres

1 + 3 + 3^2 ...+3^(n-1) = 3^n - 1/2 2012-01-27
From Vicki:
I am trying to find out how to do show how this proof was worked.
Here is the end result 1 + 3 + 3^2 ...+3^(n-1) = 3^n - 1/2

This equation was used to find the number of white triangles in the Sierpinski Triangle

The sum of a series 2011-11-07
From Rattanjeet:
Find the sum of 1(1/2) + 2(1/4) + 3(1/6) + 4(1/6)(3/4) + 5(1/6)(3/4)2 + 6(1/6)(3/4)3+ ... where 1/6 + (1/6)(3/4) + (1/6)(3/4)2 + ... constitutes a geometric series.
Infinite Logarithmic Series 2011-08-08
From Sourik:
Dear Expert,

In my Amithabha Mitra and Shambhunath Ganguly's "A Text Book of Mathematics" I found the formula of log (1+x) where the base is e and x lies in between -1 and +1.As I want to learn Mathematics,I am not satisfied with the mere statement of the formula.Please help giving me the full proof.
Thanking you,
Sourik

An imaginary infinite geometric tree 2011-02-18
From Elise:
An imaginary infinite geometric tree grows 1m the first day. 2nd day 2 branches and right angles to each other and each 0.5 m long. 3rd day two new branches at ends of each of previous days' 2 branches, again at right angles, and only .25m long each.
And so on, infinitely.
Q: Use relationships of right-angled triangles and high school level knowledge of geometric series to show the tree height is limited to (4 + sqrt2)/3 m and width to (2(sqrt2 + 1))/3 m.

A Taylor polynomial for (lnx)/x 2010-09-29
From Dave:
I have a series problem that I cannot solve. The problem asks for you to compute a Taylor polynomial Tn(x) for f(x) = (lnx)/x. I calculated this poly out to T5(x) and attempted to use this to identify a pattern and create a series in order to calculate Tn(x). However, the coefficients on the numerator out to F5prime(x) are as follows: 1, -3, 11, -50, 274... Ok, so the negative is an easy fix -> (-1)^n-1. But the other coefficients are stumping me. I can't see any sort of pattern there and I've tried every trick I know. Is there another way to go about this? Thanks!
A geometric progression 2010-04-30
From Kalyani:
sum of infinite geometric progression is 9 and common ratio is 1/10 then sum up to 8 terms is?
1/1+1/2+1/3... 2010-03-31
From Mohd:
you explained the way of getting the summation of 100 series numbers but what is the summation of the numbers 1/1+1/2+1/3+1/4+1/5.............................+1/100
A sequence of letters and numbers 2009-11-10
From Maria:
What is the last ten letters and numbers in the following series and how do I work it out so I can explain it to an eleven year old. J1F8M1A0M1J0J1
Answered by Robert Dawson, Claude Tardif and Harley Weston.
An infinite geometric series 2009-05-18
From terri:
find the sum of the infinite geometric series

14 -7 +7/2 -7/4 +.....

A. 7007/13 B. 2002 C. 28/3 D.5005/7

2+6+12+20+30+42 2009-04-24
From fredy:
what is the sigma notation for the series 2+6+12+20+30+42?
The ratio test 2009-03-06
From Haley:
Use the ratio test to determine whether the series in convergent or divergent. (2/5)+(4/10)+(8/15)+...
Convergent or divergent? 2009-03-03
From Betsy:
Use the ratio test to determine if the series is convergent or divergent. 1+1/2^2+1/3^3+1/4^4

I know the general terms are a(n)=1/n^n and a(n+1)=1/(n+1)^(n+1) but I can't simplify r=lim(n->inf.)=n^n/(n+1)^(n+1)

The middle term of an arithmetic sequence 2008-12-15
From Leigh:
Find the sum of the first fifteen terms of an arithmetic series if the middle term is 92
An arithmetic series 2008-10-17
From Laura:
In an arithmetic series 5+9+13+...+tn has a sum of 945. How many terms does the series have? What formula do I use?
Demographics 2008-07-25
From shahrukh:
Each year for 10 years ,the population of a city increased by 5% of its value in the previous year. If the initial population was 200 000 ,what was the population after 10 years ??
A series solution of y' = xy 2008-07-03
From sasha:
I've to find the power series solution of the differential equation: y' = xy.

What number best completes the series? 2007-11-12
From Grace:
What number best completes the series?

2 3 7 13 27 ____

Answered by Stephen La Rocque, Penny Nom and Harley Weston.
Applications of sequences and series 2007-08-27
From Trish:
I'm a grade 12 learner working on a math project based on sequences and series. I'd like to know the different types of sequences and series such as fibonacci, fourier, farey, etc.

I've already used the Fibonacci Sequence and Harmonic Series and need two more. The simpler the sequence or series type the better.

I'd also like to know in which non-mathematical areas use sequences and series and how. Areas such as engineering or science.

A sequence of circles 2007-06-11
From Ann:
Please help with solving the following problem!!! A circle is inscribed in an equilateral triangle with a side of length 2. Three circles are drawn externally tangent to this circle and internally tangent to 2 sides of the triangle. 3 more circles are drawn externally tantgent to these circles and internally tangent to 2 sides of the triangle. if this process continued forever, what would be the sum of the areas of all the circle? the answer 1 parent came up with was Pie over 2, but we don't know how he did it. Can you please show the work or explain the answer to this problem? Thank you Ann p s my daughter is in 9th grade math.
Answered by Steve La Rocque, Chris Fisher and Penny Nom.
A geometric series 2007-04-03
From jessica:
If a geometric series includes 54-18+6-2 as its fifteenth through eighteenth terms, find the sum of the second through the fifth term, inclusive.
Arithmetic Series 2007-02-18
From Krista:
Question- The sum of the first 4 terms of an arithmetic series is -8 and the sum of the first 5 terms is 500. Determine the sum of the 3 terms.
An arithmetic series 2006-11-28
From Jillian:
Find the sum of 21 terms of an arithmetic series that has an eleventh term equal to 30.
Sigma from 0 to infinity of (n^3 / 3^n) 2006-11-15
From Cedric:
I'm wondering how you would find if this series converges or diverges?

Sigma from 0 to infinity of (n^3 / 3^n)

Does the n^3 dominate, or does the 3^n dominate? What about higher powers like n^10 / 10 ^ n ? Which one would dominate then?

From Lisa:
When I have a total that is the sum of consecutive numbers, how do I figure out what the numbers are?
Arithmetic Sums 2006-04-12
From Angel:
(a) In a particular arithmetic sequence, u6 = 344.5 and u20 = 88.3. Find S28. (b) In a particular arithmetic series, S10 = 495 and S15 = 1005. Express S15 in sigma notation.
Sum of a Geometric Sequence 2006-04-11
From Andre:
In a particular geometric sequence, U3=-3.6 and U10=12.9. Find S16 and S17.
Arithmetic progressions 2006-01-31
From A student:
1)the sum to n terms of a particular series is given by Sn=17n-3n2

a)find an expression for the n term of the series
b)show that the series is an arithmetic progression

2)a particular arithmetic progression has a positive common difference and is such that for any three adjacent terms ,three times the sum of their squares exceeds the square of their sum is 375.Find the common difference

An Arithmetic sequence 2005-12-01
From Aana:

The first term in an arihmetic series is 25 and the 3rd term is 19. Find the number of terms in the series if its is 82.

Here's what I did to find d
a+2d=19; 25+2d= 19 ;19-25=2d d=-6/2=-3

This is where I'm stuck. Can you please provide me with some guidance.

The sum of a series 2005-08-31
From Aamod:
Find the sum of the given series till n terms:

(14\1*3) + (24\3*5) + (34\5*7)............... till n terms

The Maclaurin series generated by f(x)=x^ cosx + 1 2005-08-10
From Latto:
f(x)=x3·cosx + 1. but when I take the derivatives, I couldn't see a pattern. Can you help?
A geometric sequence 2005-06-21
From A student:

The first three terms of a geometric series are 3(q+5), 3(q+3), (q+7) respectively.
Calulate the value of q.

A Taylor series for ln(x) 2005-04-16
From Anood:
i have to represent ln(x) as a power series about 2

i`m not getting the final answer which is ln 2+ sigma (((-1)(n+1)/ (n*2n))*(x-2)n). i don`t get the ln 2 part

i show you my trial

f(x)= ln x.

f-(x)=(1/x) .

f--(x)= (-1/x2)*1/2!

f---(x)= (2/x3)*1/3!

f----(x)= (-6/x4)* 1/4!

so the pattern shows me that f(n)= ((-1)(n+1))/xn *n)

so f(2)= sigma ((-1)(n+1))/2n *n) *(x-2)n

so as you see i don`t get ln 2

Sum to n terms of the series i.(2^(n-i)) 2005-01-28
From Satya:
Sum to n terms of the series i.(2n-i)
The third derivative 2004-10-15
From Holly:
Why would you ever take the third derivative?
The series from i=1 to n :ai 2004-08-18
From Ken:
a.) Explain the difference between
the series from i=1 to n :ai
and the series j=1 to n :aj

b.) Explain the difference between
the series from i=1 to n:ai
and the series from i=1 to n :aj

Programming without trig functions 2004-05-25
From Derek:
I am a programmer trying to calculate the following.

What is the formula to find the cross-sectional area of a cylinder with out using any trig functions? or better yet, how can you calculate any given volume in a cylindrical tank with spherical heads with out trig functions?

I am using a PLC (programmable logic controller) to do this and trig functions are not available.

A geometric sequence 2004-04-13
From Michael:
In a geometric series, the sum of the 2nd and 3rd terms is 60, and the sum of the 3rd and 4th terms is 240. Find the sum of the first 7 terms.
Cosine of 35 degrees 2004-03-03
From Jason:
How do you find the exact solution to cosine 35 degrees.
A worm crawling home 2004-02-18
From Cindy:
A worm is crawling to his home which is one meter away. The longer he crawls the weaker he gets and the less he can crawl the next day. If he crawls within 1/3000 of a meter of his home, he will find food. He must eat within twelve days. The first day he crawls 1/2 meter. The second day he crawls 1/4 meter. The third day he crawls 1/8 of meter. This pattern continues for twelve days. Make a Chart that shows the distance he has covered at the end of each day and the total he has covered at the end of each day. Does he make it to the Food in time?
From Joel:

I have this project to do about crosses and I can't think of what the answer is for the following questions: What is the area rule of the crosses (the table below will help you)?
Cross NumberArea sq cm
15
213
325
441
561

I also need to know what the formula is for it?

Chopping trees 2003-04-19
From Tamara:

The master needs some of the trees (twenty, to be exact) at the back of his spooky old mansion cleared to make way for a new evil laboratory, so he decides to send some his slaves to do the work for him.

He initially sends out four of his men, armed with axes, to chop the trees down. Due to the fact he is very impatient, every ten minutes he sends out another man to help with the work.

Assuming that it takes one man 30 minutes to chop down 1/3 of a tree, how long till all twenty trees are chopped down?

The sum of the first 1000 even integers 2003-02-06
From Jill:
What is the sum of the first 1000 even integers?
Arithmitic sequence 2003-02-01
From A student:
I am having problems solving this arithmetic sequence... 1, 5, 10, ___, 50, 1.00, ___, 10.00, ... I believe the answers to be 25 and 5.00 but I can't figure why.
1+2+3+...+500 2003-01-31
From Brian:
What is the sum of the numbers from 1 to 500 inclusive?
A bouncing ball 2002-12-14
From Eman:

Q : When a childís ball is dropped from a height h metres on to a hard, flat floor, it rebounds to a height of 3/5h metres. The ball is dropped initially from a height of 1.2m.

1. Find the maximum height to which the ball rises after two bounces.
2. Find the total distance that the ball has traveled when it hits the floor for the tenth time.
3. Assuming that the ball continues to bounce in the same way indefinitely, find the total distance that the ball travels.

7+8+9+...+1000 2002-09-11
From Shirley:
My question is what is the formula for adding up numbers when you don't start with number 1? For example 3 + 4 + 5 + 6 = 18. But how could you arrive at the answer without adding all the numbers?
My salary is doubled everyday for 30 days 2002-01-17
From Kanishk:
I recieve 1 penny the 1st day, 2 pennies the 2nd day, and my salary is doubled everyday for 30 days. How much money will I have by the end of the 30 day time period? (Is there a way of solving this problem without a chart?)
A geometric series 2001-10-24
From Tashalee:
The sum of the first 3 terms of a geometric series is 13. The sum of their reciprocal is 13/9. how do you find the first three terms?
Harmonic numbers 2001-05-23
From Leslie:
The harmonic numbers Hk, k = 1,2,3.....are defined by Hk = 1 + 1/2 + 1/3....1/k

I am trying to prove by mathematical induction:

H2n >= 1 + n/2 , whenever n is a nonnegative integer.

H8 = H23 >= 1 + 3/2

Can you help?

A Taylor series 2001-04-27
From Karan:
Given the following information of the function
1. f''(x) = 2f(x) for every value of x

2. f(0) = 1

3. f(0) = 0
what is the complete Taylor series for f(x) at a = 0

Geometric and arithmetic sequences 2001-01-26
From Garry:
what are the equations for geometric and arithmetic sequences?

also, what are the equations for finding the sums of those series?

Answered by Leeanne Boehm and Penny Nom.
An infinite series 2000-12-16
From John:
summation(n=1 to infinity)[n sin(1/(2n))]n
Power series representations 2000-11-27
From Grace:
Is there a systematic way of finding a power series representation of a function? I understand that you have to manipulate the function so that it is of the form 1/(1-x), but beyond that I am lost.
Comparing an integral and a sum 2000-11-21
From Douglas Norberg:
A fellow teacher asked me about a problem she wanted to give to her students. It involved whether to take a million dollars or a penny doubled a number of times. I was able to determine the number must have been .01 * 230 which is about \$10 million and a lot more than \$1 million. To check that I was right I used a spreadsheet and did a Riemann sum.

When I finished I reasoned that I had done the task in several steps and I could have done it in 1 step. Thus I integrated .01 * 2x from 0 through 30 but the number I got was \$15,490,820.0324. Why the difference?

Infinite Geometric Series 2000-11-10
From Sam Carter:
I ran into a problem when studying how to find the sum of an infinite geometric series. My math book attempts to explain the concept by giving formulas involving sigma and |r|, but it does not really explain how to go about finding the sum of an infinite geometric series. If you could either help me with this or point me in the direction of an informative website that could help me, I'd appreciate it.
Maclaurin series again 2000-09-23
From Jason Rasmussen:
I suppose my confusion comes into play when I am trying to figure out where the xn term comes from. I know that the Power Series notation is directly related to the Geometric Series of the form sigma [ brn ] where the limit is b/(1-r) for convergence at | r | <1. Therefore, the function f(x) needs to somehow take the form of b/(1-(x-a)), which may take some manipulation, and by setting r = (x-a) and b = Cn, we get the Geometric Series converted to the Power Series. Taking the nth order derivative of the Power Series gives Cn = fn(a)/n!. There must be a gap in my knowledge somewhere because I cannot seem to make f(x) = ex take the form of f(x) = b/(1-(x-a)). Maybe I should have labelled my question as "middle" because it may be more of a personal problem with algebra and logarithms. Or, am I to assume that all functions can be represented by sigma [fn(a) * (x-a)n / n!]?
A Maclaurin series 2000-09-21
From Jason Rasmussen:
I have a question regarding power series notation for certain functions within the interval of convergence.
7 - - - - 77 2000-09-13
From Peter:
Does anyone know how to solve the following:
7 _ _ _ _ 77 ?

I have to find the missing values.

Answered by Chris Fisher and Walter Whiteley.
1+4+9+16+...n^2 = n(n+1)(2n+1)/6 2000-06-01
From Shamus O'Toole:
How do you derive that for the series 1+4+9+16+25.. that

S(n)=(n(n+1)(2n+1))/6

Geometric sequences 2000-04-11
From Jodie:
I am in a grade ten principles class and was taught how to do geometric sequences and series but no one in my class understood what we were taught. Our teacher is one of few to use the new curriculum which used to be the grade twelve curriculum. Could you please explain to me how to do geometric sequences and how to find the different terms and sums. Thank you very much!
Approximations 1999-12-20
Long-time ago I red an article about surprizing (and in a way frustrating) results in math, for example the limit of a nicely defined infinite series which was believed to be a simple rational number, but later was determined to be a transcendent number that missed the rational value by an incredibly small amount (so for example the limit proved to be 2.75000...00137.. with a lot of 0's in between). I cannot find that article anymore, so i was wondering if you have any such examples, or you can point to any relevant information source?
From Nowl Stave:
Why is the radius of convergence of the first 6 terms of the power series expansion of x^(1/2) centered at 4 less than 6?
A Series 1999-04-20
From Deepak Shrestha:
Given the sequence an=e^(-n*Ln(n)), does the series converge and why?
Sequences and series 1998-05-27
From Michael Le Francois:
The sum of the first ten terms of an arithmetic series is 100 and the first term is 1. Find the 10th term.

The common ratio in a certain geometric sequence is r=0.2 and the sum of the first four terms is 1248 find the first term.

Quel est le 6e nombre dans la serie suivante 2010-08-13
From jeff:
Quel est le 6e nombre dans la serie suivante: 1,2,6,42,1806,...
Answered by Stephen La Rocque and Claude Tardif.
Une série géométrique 2008-11-23
From anass:
je vx savoire est ce kil existe la somme de (1/n^x) avec n variant de 0 jusk à infini
nota:
lorsk x=1et 2 la somme reste tjrs facile mé lorsquil depasse 3 c difficile et merci