Prove √a(n) Converges to 0 | Stuck on Proof

[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.

 

[Mark44]

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.

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

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

 

[CoachBryan]

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

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

Yes it converges to zero

 

[deluks917]

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

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