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Math Help - Serious Series Question

  1. #1
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    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)
    Last edited by Corum; January 6th 2010 at 03:34 PM.
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  2. #2
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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 \left| r \right| < 1 \Rightarrow \quad \sum\limits_{n = k}^\infty  {r^n } \text{ converges!}
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  3. #3
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    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..
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  4. #4
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    Quote Originally Posted by Corum View Post
    Ratio test? .
    \lim _{n \to \infty } \left| {\frac{{a_{n + 1} }}<br />
{{a_n }}} \right| \to L < 1 \Rightarrow \quad \sum {a_{_n }\text{ converges!}}
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  5. #5
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    Thank you for that! I have just one more for now..

    +infinit;n=0 \frac{ n(x+3)^n}{4\exp{n+1}}
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  6. #6
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    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.
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  7. #7
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    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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