## Combinatorics - Mathematical Induction?

Hello, I am having trouble solving this problem. Maybe I'm just overreacting to it. In my two semesters in discrete math/combinatorics, I've never seen a problem like this (with two summations) and been asked to prove it. Can some one help?

$\sum^{n}_{i=1} i^3 = \frac{n^2(n+1)^2}{4} = (\sum^{n}_{i=1} i)^2$

I mean, I know the whole S(n), S(1), S(k), S(k+1) steps, but I'm just unsure of how to write it. The solutions manual for the book skip that problem.

Book: Discrete And Combinatorial Mathematics: An Applied Introduction by Ralph P. Grimaldi, 5th Edition.

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 Blog Entries: 8 Recognitions: Gold Member Science Advisor Staff Emeritus First of all, this is a textbook problem, so it belongs in the homework forums. I moved it for you Second, you actually need to show two things: $$\sum_{i=1}^n i^3=\frac{n^2(n+1)^2}{4}$$ and $$\sum_{i=1}^n i = \frac{n(n+1)}{2}$$ (and square both sides) Can you do that?
 Thank you very much! That helped a lot, I just finished my proof. :D That makes sense why you'd have to break it up. I didn't put the relationship between $\sum^{n}_{i=1}i = \frac{n(n+1)}{2}$ and $(\sum^{n}_{i=1}i)^2 = \frac{n^2(n+1)^2}{4}$ together. lol

Recognitions:
 Quote by nintendo424 Hello, I am having trouble solving this problem. Maybe I'm just overreacting to it. In my two semesters in discrete math/combinatorics, I've never seen a problem like this (with two summations) and been asked to prove it. Can some one help? $\sum^{n}_{i=1} i^3 = \frac{n^2(n+1)^2}{4} = (\sum^{n}_{i=1} i)^2$ I mean, I know the whole S(n), S(1), S(k), S(k+1) steps, but I'm just unsure of how to write it. The solutions manual for the book skip that problem. Book: Discrete And Combinatorial Mathematics: An Applied Introduction by Ralph P. Grimaldi, 5th Edition.