Arithmetic operations on sequences

[dssmith]

Homework Statement

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

Homework Equations

hint: conjigate first

The Attempt at a Solution

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

i do not own LATEX, yet.

 

[Mark44]

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

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

 

[GcSanchez05]

Clever like WHAT?? Waaaaah :'(