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Tom Mattson
Sep23-03, 06:53 PM
Sci Advisor
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Proof by Induction

But I can seem to get this part:

Assuming P(k) is true, you can cancel it from the left hand side if you also cancel the right side of P(k) from the right side of P(k+1). You should be left with an identity, which proves that P(k) implies P(k+1).
OK, note that the part in blue below is just P(k).


What you need to do is expand the right hand side of both P(k) and of P(k+1). Then, you can subtract Σj=1kj3 from the left side of the above, and you can also subtract (1/4)x2(x+1)2 from the right side of the above (since those two quantities are equal).

What you will be left with is:




which is an identity.

edit: fixed an omission