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AM GM inequality help

  1. Oct 4, 2010 #1
    1. The problem statement, all variables and given/known data

    Prove

    a)5 < 51/2 + 51/3 + 51/4

    b) n > n1/2 + n1/3 + n1/4 for all ints n>8

    2. Relevant equations



    3. The attempt at a solution
    i tried the AM GM inequality
    and found

    51/2 + 51/3 + 51/4 > 3(513/36)

    what further can i do?
    can anyone please help me out??
     
  2. jcsd
  3. Oct 4, 2010 #2

    Mark44

    Staff: Mentor

    Re: inequality

    > 3 * 51/3 = (27 * 5)1/3

    Can you show that the last expression is > 5?
     
  4. Oct 4, 2010 #3
    Re: inequality

    Thanks
    so i got that part and showed the expression > 5.

    I could prove the 2nd part by this method too!

    Thanks a lot!!! :smile:
     
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