Question

Series question

Answer 1

If the series \[\sum_{n=1}^{\infty} a_{n}\] converges, then \[\sum_{n=1}^{\infty} cos(a_{n})\] converges.

Answer 2

Is this true or false?

Answer 3

I'm pretty sure it's false, but need confirmation.

Answer 4

sum 1/n^2 converges

wolfram says sum cos(1/n^2) does not

Answer 5

I thought so. How would you provide a counter-example for the above statement? Any ideas?

Answer 6

it says to use divergence test