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Limit of sequence

  1. Mar 31, 2008 #1
    1. (a) If{an} is a covergent sequence and limit of an ^2=0, prove that limit of an=0.



    (b) If limit of an ^2=L>0 , give an example to show that limit of an =√L may not be true.



    2. For any x≧0, show by binomial theorem, that

    (1+x)^n ≧〔n(n-1)x^2〕/2 for any positive integer n.
     
  2. jcsd
  3. Mar 31, 2008 #2
    What is your atemp? To help you:

    What can you say about the function f(x) = x^2.

    If I in (b) tell you that you could actually say that if Lim a_n = sqrt(L) then you actually get Lim a_n^2 = L, what condition does the sequence in (b) have to satisfy to give the counter example.
     
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