# Arithmetic operations on sequences

1. Sep 30, 2009

### dssmith

1. The problem statement, all variables and given/known data

If the sequence {a_n} n=1 to infinity converges to (a) with a_n >0 show {sqrt(a_n)}
converges to sqrt(a)
2. Relevant equations

hint: conjigate first

3. The attempt at a solution

abs[ (a_n-a) / (sqrt(a_n)+sqrt(a) ) ] < epsilon

i do not own LATEX, yet.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Sep 30, 2009

### Staff: Mentor

You know that for some M, and for all n >= M, there is a positive epsilon such that |an - a| < epsilon.

I would approach this by factoring |an - a| into $|\sqrt{a_n} - \sqrt{a}||\sqrt{a_n} + \sqrt{a}|$. Then maybe you can replace the second factor by something clever.

3. Dec 4, 2011

### GcSanchez05

Clever like WHAT?!?! Waaaaah :'(