How to show if lim goes to 0 then square root of it goes to zero

Question

I've got a few exercises from a teacher to work with lim.

Task is exactly as title say, but more formaly $a_n \rightarrow 0$ then $a_n^{1/k} \rightarrow 0$ My only idea was too show that $a_n = \frac{p}{q}$ then if $a_n \rightarrow 0$ then it implies that $q>p$, so $q^{1/k} > p^{1/k}$ for any k. But i have a feeling that is not fully correct. Could you help me out with this? Thanks in advance :-)

No, that doesn't look so promising. You seem to be assuming each $a_n$ is rational. — dfeuer, Nov 29 '13 at 00:03

score 3 · Accepted Answer · edited Jun 12 '20 at 10:38

3

Hint

Use an explicit $\epsilon$-$\delta$ argument. You will have to specify the problem a bit more carefully for even $k$.

edited Jun 12 '20 at 10:38

Community

1

answered Nov 29 '13 at 00:09

dfeuer

9,069

How to show if lim goes to 0 then square root of it goes to zero

1 Answers1

Hint