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Math Help - Mathematical induction

  1. #1
    Junior Member
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    Mathematical induction

    (*) For all natural numbers n, 1 + 2 + 3 + 4 + ... + n = (n)(n+1)/2

    Assume for k:

    ... + k = (k)(k+1)/2

    Assume for k+1:

    ... + k+1 = (k+1)(k+2)/2

    I believe I need to increment the series to actually create a valid test:

    ... k + k+1 = (k+1)(k+2)/2

    Hmm.. the sides don't seem to match, where did I go wrong?
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  2. #2
    Senior Member Twig's Avatar
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    First you prove that it holds for n=1.

     1 = (1)(1+1)\frac{1}{2} = 1 \; \mbox{ ok! }

    Now you assume that it holds for k, and prove that it holds for k+1.

     1+2+3+ \dots k + (k+1)=k(k+1)\frac{1}{2}+(k+1)

    If you write the right side with common denominator:

     \mbox{Right side: } \frac{1}{2}(k(k+1)+(k+1)) = \frac{1}{2}(k+1)(k+2)

    And you´re there.
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