1. ## Geometric Series

I'm having trouble finding r in these two problems.

$\displaystyle \sum_{n=1}^{\infty} {\frac{n}{n+1}}$

and

$\displaystyle \sum_{n=0}^{\infty} {sin^n(\frac{\pi}{4}+n{\pi})}$

2. Originally Posted by CarDoor
I'm having trouble finding r in these two problems.

$\displaystyle \sum_{n=1}^{\infty} {\frac{n}{n+1}}$

and

$\displaystyle \sum_{n=0}^{\infty} {sin^n(\frac{\pi}{4}+n{\pi})}$

Who told you they are geometric?

3. The first serie doesn't converges, and in the second, you can use that $\displaystyle \sin(\frac{\pi}{4}+n\pi)=\sin(\frac{\pi}{4})\cos(n \pi)+\sin(n\pi)\cos(\frac{\pi}{4})$

4. If they're not geometric, how would I find whether they converge or diverge?

5. Originally Posted by CarDoor
If they're not geometric, how would I find whether they converge or diverge?
So is the question meant to be "Find whether the following series converge or diverge"? You've already been told the answer to the first - the reason is that $\displaystyle \lim_{n \to +\infty} \frac{n}{n + 1} \neq 0$.

It would have saved the time of everyone if you did not provide a misleading post title.