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Induction, tough one

  1. Oct 14, 2008 #1


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    just joined the forum

    1. The problem statement, all variables and given/known data

    n(1/n) > (n+1)1/(n+1) for all n>=3.

    2. Relevant equations

    3. The attempt at a solution

    k1/k > (k+1)1/(k+1)

    => k > (k+1)k/(k+1)
    => k+1 > (k+1)k/(k+1) + 1
    => (k+1)1/(k+1) > [(k+1)k/(k+1) + 1]1/(k+1)

    I then tried binomial expansion of the term on the right.
    leads to

    (k+1)1/(k+1) > (k+1)k/(k+1)2 + 1/(k+1)*(k+1)[k/(k+1)][1/(k+1) -1] + (-k)/(2(k+1)2)*(k+1)[k/(k+1)][1/(k+1) - 2].....

    But seem to be getting nowhere because of the negative term that appears and will continue to appear in every other term...
    Am i on the right path?

    apologies if it is too easy.
  2. jcsd
  3. Oct 14, 2008 #2


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    and btw, i've figured out how to do it without using induction.
    but i want to know how to prove it using induction
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