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Math Help - Power Series Question

  1. #1
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    Power Series Question

    Question: What is the radius of convergence for the power series:  $\displaystyle\sum\limits_{n=0}^\infty \sqrt{n(n+1)}(\pi t+7)^{n}$

    I am totally not sure about how to solve this question. I have learned techniques of ratio test and also root test. I need a jump start!

    Thanks.
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  2. #2
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    \displaystyle r=\lim_{n\to\infty}\left|\frac{c_n}{c_{n+1}}\right  |
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  3. #3
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    Does the n = 0 make a difference since usually the questions have n = 1. Also for the ratio test since it  \displaystyle r=\lim_{n\to\infty}\left|\frac{c_{n+1}}{c_{n}}\rig  ht|
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  4. #4
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    Just run the limit as it is shown.
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  5. #5
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    So which formula is correct? The one you showed or the one i replied with?
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  6. #6
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    You are correct. Sorry about that.
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  7. #7
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    Ok, i'll give that a try then!
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  8. #8
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    I got  L = |\pi t +7| , so since we want to have series convergence,  R = 1 ?

    Since,   |\pi t +7| < 1 series converges and  |\pi t +7|  > 1, series diverges?
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