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Math Help - Geometric Series

  1. #1
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    Geometric Series

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

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

    and

    \sum_{n=0}^{\infty} {sin^n(\frac{\pi}{4}+n{\pi})}
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  2. #2
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    Quote Originally Posted by CarDoor View Post
    I'm having trouble finding r in these two problems.

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

    and

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

    Who told you they are geometric?
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  3. #3
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    The first serie doesn't converges, and in the second, you can use that \sin(\frac{\pi}{4}+n\pi)=\sin(\frac{\pi}{4})\cos(n  \pi)+\sin(n\pi)\cos(\frac{\pi}{4})
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  4. #4
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    If they're not geometric, how would I find whether they converge or diverge?
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  5. #5
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    Quote Originally Posted by CarDoor View Post
    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 \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.
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