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Math Help - Mathematical Induction

  1. #1
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    Mathematical Induction

    Hey, i have a question here that reads:

    Prove by mathematical induction that 1 + 1 + ... + n = (n(n+1))/4 for any natural number n.

    Could anyone get me started on this? Any help would be greatly appreciated. Thanks.
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  2. #2
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    Quote Originally Posted by GreenDay14 View Post
    Hey, i have a question here that reads:

    Prove by mathematical induction that 1 + 1 + ... + n = (n(n+1))/4 for any natural number n.

    Could anyone get me started on this? Any help would be greatly appreciated. Thanks.

    Don't you mean 1^3+2^3+3^3+...+n^3
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  3. #3
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    Nope, reading it straight out of the book.
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  4. #4
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    the expression 1^3+1^2+...n^3 doesnt make any sense


    I will assume the book/you actually want to prove \sum_{k=1}^n k^3=\frac{n^2(n+1)^2}{4} which is true, can you prove this now that I have stated the actual problem or do you still need help
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  5. #5
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    You can look at a similar thread here.
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  6. #6
    Junior Member guildmage's Avatar
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    Could you verify the first three steps? For n = 1, n = 2, and n = 3.
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  7. #7
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    I think there might be a typo because in this problem you can't prove the base case for your proposition:

    P(1) = \frac{1^2(n+1)^2}{4} = 1 \neq (1^3 + 1^2 + 1) = 3

    If we can't prove the base case, we can't move onto the inductive step.
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