I'm trying to solve this problem from CH2 of spivak's calculus of which I am self-studying.(adsbygoogle = window.adsbygoogle || []).push({});

1. The problem statement, all variables and given/known data

Prove the following by mathematical induction:

[tex]1^3+...+n^3=(1+...+n)^2[/tex]

2. Relevant equations

To prove by mathematical induction, you test whether P(1) is true and if P(k) is true then P(k+1) is true.

3. The attempt at a solution

[tex]1^3+...+n^3=(1+...+n)^2[/tex]

[tex]1^3+...+n^3+(n+1)^3=(1+...+n)^2+(n+1)^3[/tex]

[tex](1+...+n)^2+(n+1)^3=(1+...+n+1)^2[/tex]

From there I have no clue and I've been staring at that for 15 minutes.

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# Homework Help: Mathematical Induction problem

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