I am trying to prove by induction 1^3 + 2^3 + ... n^3 = [n(n+1)/2]^2(adsbygoogle = window.adsbygoogle || []).push({});

when n is a positive integer

Let P(n), if P(1) then n^3 = 1^3 = 1 and [n(n+1)/2]^2 = [1(1+1)/2]^2 = 1

the inductive hypothesis is 1^3 + 2^3 + ... k^3 = [k(k+1)/2]^2

Assuming P(k) is true then prove P(k+1) is true, insert (k+1) into problem

1^3 + 2^3 + ... k^3 + (k+1)^3 = [k+1(k+1+1)/2]^2 or [(k+1)(k+2)/2]^2

by the inductive hypothesis we get

[k(k+1)/2]^2 + (k+1)^3 = [(k+1)(k+2)/2]^2

am I thinking this through correctly? and where do I go from here?

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# Homework Help: Induction problem

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