Prove Limit of Sequence 1 and Show Binomial Theorem

[chiakimaron]

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.

 

[mrandersdk]

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.