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Math Help - Prove that there is a unique positive integer greater than 1 that equals

  1. #1
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    Prove that there is a unique positive integer greater than 1 that equals

    I don't know how to solve this problem.

    Prove that there is a unique positive integer greater than 1 that equals

    the sum of the positive integers less than it.

    I started of as

    condition 1: n>1

    condition 2: sum = n - 1

    I'm stuck
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  2. #2
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    Quote Originally Posted by HelpMehPlz View Post
    I don't know how to solve this problem.

    Prove that there is a unique positive integer greater than 1 that equals

    the sum of the positive integers less than it.

    I started of as

    condition 1: n>1

    condition 2: sum = n - 1

    I'm stuck
    The second condition is : n = (n-1)+(n-2)+(n-3)+...+1 .
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  3. #3
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    Quote Originally Posted by HelpMehPlz View Post
    Prove that there is a unique positive integer greater than 1 that equals
    the sum of the positive integers less than it.
    M = \sum\limits_{k = 1}^{M - 1} k  = \frac{{\left( {M - 1} \right)M}}<br />
{2}\; \Rightarrow \;M = 3
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