Hi,

Still me with some limit problems...

Now I just don't any clues about what to do with trigonometric functions...

I have this :

$\displaystyle \sum_{n=1}^{\infty}sin(\frac{1}{n}) - sin(\frac{1}{n+1})$

I know it becomes this :

$\displaystyle \sum_{n=1}^{\infty}sin(\frac{1}{n}) - \sum_{n=1}^{\infty}sin(\frac{1}{n+1})$

I know that the first one will tend towards 0 since sin(1/infinity) = sin(0) = 0

The second one, believe it or not, I'm not so sure about how to find its limit.

But I know that the limits of those two blocks isn't the answer of the question, that I have to look at their "s_{n}"'s, but how would I be able to estimate sin(1) + sin(1/2) + sin(1/2) + ... and the other one that I won't write here ?

Same thing for the following, I'm clueless...

$\displaystyle \sum_{n=1}^{\infty}arctg(n)$

Please help, I'm kind of lost right now.