Re: Does this series converge or diverge?

In article
<0c3761cb-a458-47a5-b3fb-537372c6e881@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
nicegirl_130@xxxxxxxxx wrote:

\Sum(n =1, oo) (1 + sin(n))/sqrt(n).

I tried everythiing I know, but nothing worked, total frustration.
Is the fact that sin(n) is dense in [0, 1] useful here?

Hint: For each m = 1, 2, ... , there must be an integer between 2Pi*m
and 2Pi*m + Pi; choose one of them and call it n_m. The sum of your
series is at least as big as Sum(m=1,oo) (1 + sin(n_m))/sqrt(n_m).
.