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Squeeze Theorem Problem

  1. Oct 25, 2007 #1
    1. The problem statement, all variables and given/known data
    Use the squeeze theorem to prove the sequence converges to 0. (Given the lim 1/n=0 and 1/n^2=0.

    A) cos n pi / n^2

    B) ((-1)^n) ln(n) / n^2

    I know you have to show that the sequence "squeezes" between the two given above, but I am having problems doing so, any help would be great. Thanks.
     
    Last edited: Oct 25, 2007
  2. jcsd
  3. Oct 25, 2007 #2
    Although your notation is a little ambiguous i am assuming that on A) you meant

    ( cos(npi) )/n^2

    remember that
    0<=Icos(npi)I<= 1, i am assuming also that n is from naturals, than we can safetly multiply by 1/n^2 (or devide by n^2) because it is also positive, (moreover n^2 is always positive regardless of the sing of n) then we get:

    0<=Icos(npi)I/n^2 <= 1/n^2 now taking the limit when n--> infinity what do u get?

    Next time show your work, before the people here can give you any help.

    B) use the same reasoning here also.
     
    Last edited: Oct 26, 2007
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