# Limit of sequence

1. Mar 31, 2008

### 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.

2. Mar 31, 2008