1. ## Serious Series Question

Series problem.
+infinity,1 (n!/7^n)
and
(1/(sin(-3))^n)
divergent? convergent?
Any Help will be greatly appreciated (sorry, haven't mastered LateX yet)

2. For the first one use the ratio test. It is easy to use in this case.

For the second realize that $\left| r \right| < 1 \Rightarrow \quad \sum\limits_{n = k}^\infty {r^n } \text{ converges!}$

3. OK, i've got the second one. Ratio test? I don't know if I use a foreign term or if i'm just being stupid..

4. Originally Posted by Corum
Ratio test? .
$\lim _{n \to \infty } \left| {\frac{{a_{n + 1} }}
{{a_n }}} \right| \to L < 1 \Rightarrow \quad \sum {a_{_n }\text{ converges!}}$

5. Thank you for that! I have just one more for now..

+infinit;n=0 $\frac{ n(x+3)^n}{4\exp{n+1}}$

6. If you are asked to do these, then why do you not know the material?

Given $a_n=\frac{n(x+3)^n}{4e^n +1}$ then solve this $\lim _{n \to \infty } \left| {\frac{{a_{n + 1} }}{{a_n }}} \right| < 1$ for $x$.

7. Lack of practice. Sort of, i'm preparing for an exame next week.. thank you for your help, with the first push i'm OK