# How do you show that if a(n) >= 0 for all n in N and a(n) = 0, then √a(n) Converges to 0

1. Nov 5, 2014

### CoachBryan

I've been messing with this proof for while and I'm stuck on this. I've started with a(n) converges to 0, let epsilon > 0, then there exists an n0 in N such that for all n >= n0.

I'm stuck here thus far. Any help? Thanks for your time.

2. Nov 5, 2014

### Staff: Mentor

The rest of your thought is
For all n >= n0, $\sqrt{a_n} < \epsilon$.

What are the given conditions? Is it an converges to 0? You have an = 0 in the title.

3. Nov 5, 2014

### CoachBryan

Yes it converges to zero

4. Nov 5, 2014

### deluks917

Can you prove that sqrt(an) is eventually less than 1/100 ?

How about that sqrt(an) is eventually less than 1/(1000000) ?