







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. 





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. 





cos(n)pi = (1)^n 
20061214 

From Idrees: How can I prove the following: cos(n)pi = (1)^n Answered by Steve La Rocque. 





A proof by induction 
20061002 

From Zamira: i'm studying induction but i don't get how to proof that 1+2+2^2+2^3+...+2^(n1) = (2^n)  1. Answered by Penny Nom. 





Proof by induction 
20060424 

From Meshaal: Find an expression for:
13+5  7 + 9  11 + ... + (1)^(n1) * (2n1)
and prove that it is correct.
Answered by Stephen La Rocque. 





Proving a summation formula by induction 
20060419 

From Sharon: Prove by induction that the sum of all values 2^i from i=1 to n equals 2^(n+1)  2 for n > 1. Answered by Stephen La Rocque. 





A proof by induction 
20060409 

From Sharon: prove by induction: For every n>1, show that
2 + 7 + 12 + ...+ (5n3) = n(5n1)/2 Answered by Penny Nom. 





Proof by induction? 
20050810 

From Peter:
I am a lecturer and am having a problem with the following Proof by
Induction.
If
(N x N x N x N) + (4 x N x N x N) + (3 x N x N) + (N) = 4000
Prove that N is even!
Answered by Chris Fisher and Penny Nom. 





Proof by induction 
20041120 

From Vic: Problem: Find the first 4 terms and the nth term of the infinite sequence defined recursively as follows:
a(1) = 3 and a(k+1) = 2a(k) for k > 1.
Note: Quantities in brackets are subscripts
> means 'equal to or greater than'.
Using the recursive formula, the first 4 terms are;
a(1) = 3, a(2) = 6, a(3) = 12, a(4) = 24
The nth term a(n) = 2n1 x 3 (equation 1)
Equation 1 must be proven using mathematical induction. This is where I am having a problem. Answered by Penny Nom. 





n! > n^2 
20040330 

From Jose: How can you prove by mathematical induction that:
n! > n2. Answered by Penny Nom. 





Proof by induction 
20040302 

From Chris: I need some help of how to solve the problem
"use the principle of mathematical induction to prove that the following are true for all positive integers"
cos(n x pi + X) = (1)^n cosX
any help would be appreciated Answered by Penny Nom. 





Proof by induction 
20020926 

From Pooh: Use induction to show that
1^{ 2} + 2^{ 2} + .....+n^{ 2} = (n^{ 3})/3 + (n^{ 2})/2 + n/6 Answered by Paul Betts. 





Proof by induction 
20020831 

From Tabius: Use mathematical induction to prove that the following formulae are true for all positive integers: a) 1 + 3 + 5+...+(2n  1) = n^{ 2} b) 2^{ n} > n. Answered by Penny Nom. 





Proof by induction 
20020220 

From Tamaswati: How do I prove the assertion that "the determinant of an upper triangular matrix is the product of the diagonal entries" by mathematical induction? (Before I check this assertion for a few values of n how do I rephrase the assertion slightly so that n appears explicitly in the assertion?) Answered by Penny Nom. 





Proof by induction 
20011016 

From John: Can you help me with any of these?  For any natural number n > 1, prove that
(4^{n}) / (n + 1) < [(2n)!] / [(n!)^{2}].
 For any natural number n > 1, prove that
1/sqrt(1) + 1/sqrt(2) + 1/sqrt(3) + ... + 1/sqrt(n) > sqrt(n).
 For any natural number n and any x > 0, prove that
x^{n} + x^{n  2} + x^{n  4} + ... + x^{n} >= n + 1. Answered by Penny Nom. 





Proof by induction 
20010930 

From Kyle: I'm trying to learn induction and I need to see how this done please help with this problem... 2^{0} + 2^{1} + 2^{2} +... + 2^{n} = 2^{n+1} 1 is true whenever n is a positive integer. Answered by Penny Nom. 





Harmonic numbers 
20010523 

From Leslie: The harmonic numbers H_{k}, k = 1,2,3.....are defined by H_{k} = 1 + 1/2 + 1/3....1/k I am trying to prove by mathematical induction: H_{2n} >= 1 + n/2 , whenever n is a nonnegative integer. H_{8} = H_{23} >= 1 + 3/2 Can you help? Answered by Harley Weston. 





Induction 
20000907 

From Joe Peterson: How do I prove by the principal of mathematical induction? 1.n+2.(n1)+3.(n2)+.....+(n2).3+(n1).2+n.1=(n(n+1)(n+2))/6 Answered by Paul Betts. 





Induction 
20000316 

From William Tsang: I am trying to prove a induction question Sigam r=1 n (2r 1)cube = n square (2 n square  1) Answered by Harley Weston. 

