1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Induction, tough one

  1. Oct 14, 2008 #1


    User Avatar

    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


    User Avatar

    and btw, i've figured out how to do it without using induction.
    but i want to know how to prove it using induction
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook