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)
Last edited by Corum; Jan 6th 2010 at 02:34 PM.
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For the first one use the ratio test. It is easy to use in this case. For the second realize that $\displaystyle \left| r \right| < 1 \Rightarrow \quad \sum\limits_{n = k}^\infty {r^n } \text{ converges!}$
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..
Originally Posted by Corum Ratio test? . $\displaystyle \lim _{n \to \infty } \left| {\frac{{a_{n + 1} }} {{a_n }}} \right| \to L < 1 \Rightarrow \quad \sum {a_{_n }\text{ converges!}} $
Thank you for that! I have just one more for now.. +infinit;n=0 $\displaystyle \frac{ n(x+3)^n}{4\exp{n+1}}$
If you are asked to do these, then why do you not know the material? Given $\displaystyle a_n=\frac{n(x+3)^n}{4e^n +1} $ then solve this $\displaystyle \lim _{n \to \infty } \left| {\frac{{a_{n + 1} }}{{a_n }}} \right| < 1$ for $\displaystyle x$.
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
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