(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Prove that: 1^3 + 2^3 + ... + n^3 = (1 + 2 + ... + n)^2 for all n where n is a natural number

2. Relevant equations

Proof by induction:

a) p(1) is true

b) assume p(k) is true then prove p(k+1) for it

3. The attempt at a solution

I gave this a try for a while but I'm quite stuck.

So far using proof by induction:

p(1) = 1^3 = 1^2 is true

assume that p(k) = 1^3 + 2^3 + ... + k^3 = (1 + 2 + ... + k)^2 is true

then:

p(k+1) = 1^3 + 2^3 + ... + k^3 + (k + 1)^3

= (1 + 2 + ... + k)^2 + (k + 1)^3

Now I'm really not sure where to go or if I'm going the right way. Any sort of hint would be greatly appreciated. Thanks.

-Kentt

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# Natural Numbers and Induction (Analysis with and Introduction to ProofC)

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