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Combinatorics - Mathematical Induction?

  1. Jun 15, 2012 #1
    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?

    [itex]\sum^{n}_{i=1} i^3 = \frac{n^2(n+1)^2}{4} = (\sum^{n}_{i=1} i)^2[/itex]

    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.
     
  2. jcsd
  3. Jun 15, 2012 #2

    micromass

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    First of all, this is a textbook problem, so it belongs in the homework forums. I moved it for you :smile:

    Second, you actually need to show two things:

    [tex]\sum_{i=1}^n i^3=\frac{n^2(n+1)^2}{4}[/tex]

    and

    [tex]\sum_{i=1}^n i = \frac{n(n+1)}{2}[/tex]

    (and square both sides)

    Can you do that?
     
  4. Jun 15, 2012 #3
    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 [itex]\sum^{n}_{i=1}i = \frac{n(n+1)}{2}[/itex] and [itex](\sum^{n}_{i=1}i)^2 = \frac{n^2(n+1)^2}{4}[/itex] together. lol
     
  5. Jun 15, 2012 #4

    mathman

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    These are two separate problems. ∑i³ is one and ∑i is the other. Have you tried either?

    The question belongs in mathematics, not computer science.
     
    Last edited: Jun 15, 2012
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