







Fibonacci and induction 
20100712 

From James: I'm trying to prove by induction that F(n) <= 2^(n1)
where f(1)=f(2)=1 and f(k)=f(k1)+f(k2) for k >=3 is the Fibonacci sequence Answered by Stephen La Rocque and Tyler Wood. 





A proof by induction 
20100325 

From SAMUEL: 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^(n1) log x 
20100310 

From shambodeb: This is a successive differentiation problem by Leibnitz theorem
If y = x^{n1} log x ; Proof nth derivative y^{(n)} = (n1)!/x Answered by Harley Weston. 





1^3 + 2^3 + 3^3 +4^3 ... n^3 = ? 
20100129 

From ireimaima: Hi..
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 
20100112 

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 
20091002 

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 
20090602 

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 
20080905 

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 
20080711 

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 
20080623 

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 
20080317 

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 
20080317 

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 
20080314 

From Marcelo: Prove by the principle of the math induction that:
1.3.5.7....(2n1) = (2n)!/(2^n)n! Answered by Harley Weston. 





1/(1x2)+1/(2x3)+1/(3x4)...+1/(n(n+1)) 
20080220 

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 
20071215 

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?)
Thanks. Answered by Penny Nom and Victoria West. 

