I know the first step (plugging in a number like 2) and seeing if it works, but I have trouble when it comes to inserting "k" and "k+1".

Prove by induction that

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

Any help appreciated.

Mike

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- Sep 11th 2006, 07:11 PMJaysFan31University Algebra Problem
I know the first step (plugging in a number like 2) and seeing if it works, but I have trouble when it comes to inserting "k" and "k+1".

Prove by induction that

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

Any help appreciated.

Mike - Sep 11th 2006, 07:26 PMThePerfectHacker
You have to show that,

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

Then, show that,

1+2+...+n=n(n+1)/2

Thus, since we see that if we square the bottom one then we get the top one, proof complete.

Look Heir for similar problem.