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Fibonacci and induction 2010-07-12
From James:
I'm trying to prove by induction that F(n) <= 2^(n-1) where f(1)=f(2)=1 and f(k)=f(k-1)+f(k-2) for k >=3 is the Fibonacci sequence
Answered by Stephen La Rocque and Tyler Wood.
A proof by induction 2010-03-25
use mathematical induction to proof that each statement is true for every positve integer n 1/1.2+1/2.3+1/3.4+......1/n(n+1)=n/n+1
Answered by Robert Dawson.
The nth derivative of x^(n-1) log x 2010-03-10
From shambodeb:
This is a successive differentiation problem by Leibnitz theorem

If y = xn-1 log x ; Proof nth derivative y(n) = (n-1)!/x

Answered by Harley Weston.
1^3 + 2^3 + 3^3 +4^3 ... n^3 = ? 2010-01-29
From ireimaima:
Can u please help me with this question.. I find that when i test eg: n=2 for n (n+1) /4, it seems that it does not giving me the right answer of 1^3 + 2^3 = 9 but 3/2... i'm confuse..can u please help me..thanks so much

Prove that: 1^3 + 2^3 + 3^3 +4^3..n^3 = n (n+1) /4

Answered by Penny Nom.
A proof by induction 2010-01-12
From Bhavya:
Prove by induction that if Xi >= 0 for all i, then

(Summation Xi from 1 to n)^2 >= Summation Xi^2 from 1 to n

Answered by Penny Nom.
Prove by induction 2009-10-02
From Anonymous:
How can you prove the following by induction:

Any fraction (A / B), where 0 < (A / B) < 1, can be expressed as a finite sum
(1 / c(1)) + (1 / c(2)) + (1 / c(3)) + ... + (1 / c(k)),
where c(1), c(2), ..., c(k) are natural numbers greater than 0.

[ex. (20 / 99) = (1 / 9) + (1 / 11)]

Answered by Claude Tardif.
Selecting 3 people from 4 2009-06-02
From muhammadibeaheem:
Use mathematical induction to prove that for all integers n≥1, is divisible by 3.

Question 2; A club consists of four members.How many sample points are in the sample space when three officers; president, secretary and treasurer, are to be chosen?

Answered by Penny Nom.
Mathematical induction 2008-09-05
From James:
I need to prove a problem by induction regarding the Triangle Inequality. The problem is

abs(a1 + a2 +...+an) <= abs(a1) + abs(a2) +...+ abs(an).

Answered by Victoria West.
Mathematical induction 2008-07-11
From lyn:
can you give me a basic example of a mathematical induction
Answered by Harley Weston.
The sum of the digits of a number 2008-06-23
From Ben:
Question: Using mathematical induction, prove that if the sum of the digits of a number is divisible by three, then the number itself is also divisible by 3.
Answered by Penny Nom.
n^3/3 + n^5/5 + 7n/15 is an integer 2008-03-17
From John:
Prove: For all n in Natural Numbers ( n > 1 ),
n^3/3 + n^5/5 + 7n/15 is an integer

Answered by Stephen La Rocque.
2^n > n^2 for n> 4 where n is a natural number 2008-03-17
From John:
I've been asked to prove this:
2^n > n^2 for n> 4 and n is a natural number

Answered by Penny Nom.
Induction 2008-03-14
From Marcelo:
Prove by the principle of the math induction that: = (2n)!/(2^n)n!

Answered by Harley Weston.
1/(1x2)+1/(2x3)+1/(3x4)...+1/(n(n+1)) 2008-02-20
From hossun:
Find a formula for 1/(1x2)+1/(2x3)+1/(3x4)...+1/(n(n+1)) by examining the values of this expression for small values of n. Use mathematical induction to prove your result.
Answered by Stephen La Rocque.
The Principle of Mathematical Induction 2007-12-15
From iris:
we have some confusion in our problem. Please help us. We would like to know "the principle of mathematical induction"
(i) for n=1, p(1) is true.
(ii) assume that for n=k>=1, p(k) is true we have to prove p(k+1) is true. Here (Is n=k>=1 true? or Is n=k.1 true?)

Answered by Penny Nom and Victoria West.



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