# Proving limits for converging sequences

1. Oct 23, 2004

### Ed Quanta

If a general statement like an->a where (an) is a sequence of non negative real numbers, how would we prove the sqare root an->the square root of a.

When a=0, this can easily be done. But I don't see how this is possible from the given information for the case where a>0. Thanks for any help or suggestions.

2. Oct 23, 2004

### courtrigrad

Hello

Use the fact that ( 1+ h ) ^ n > 1 + nh (corollary). We know that the sequence (an) is non negative, hence 1 + h is positive. Work of this, and you should be able to get the desired result. Try using this corollary for an = (nth rooth of n)

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook