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Math Help - mathematic induction

  1. #1
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    mathematic induction

    Hi guys im new member here in forum , i dont understand smth in solvingmath induction problems :
    it says prove that 1+1/21/2+1/31/2 +1/n1/2 > n1/2 - for n > or equal to 1 , using mathematic induction theory

    image with symbols View image: sdadadaad bmp
    thanks..
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  2. #2
    MHF Contributor
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    Re: mathematic induction

    Hey medos.

    In this kind of problems you assuming something is true for n = k and then show its true for n = k + 1. This has a domino effect in that if its true for k=1 then its true for k = 2, but if its true for k=2 then its true for k= 3 and so on.

    So what you have is Sum {k=1 to n} (1/SQRT(k)) < SQRT(n) but the sum of k+1 just adds 1/SQRT(k+1) so you have to prove that if that sum is less than SQRT(n) then the sum plus 1/SQRT(k+1) < SQRT(n+1) so If you can show that 1/SQRT(k+1) < SQRT(n+1) - SQRT(n) you're done.

    It is a little tricky if you haven't seen it before.
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