I'm stuck and not sure what I've done wrong for this problem(adsbygoogle = window.adsbygoogle || []).push({});

Prove the following by mathematical induction:

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

ok so I proved it for n = 1 and n = 2 then assume n = k

so ((k^2 + k)/2)^3

Then lets try to do n = k +1

so

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

after expanding I get

(k^6+ 9k^5+ 33k^4+ 63k^3+ 66k^2+ 36k+ 8)/8

=

(k^6 +3k^5 + 3k^4 + 9k^3 + 24k^2 + 24k + 8)/8 + k^3 + 3k^2 + 3k +1

For some reason I think that I don't have to do all of this expanding. Can someone please tell me what I"m doing wrong or what I need to fix?

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# Inductive Proof

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