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Find the radius of convergence of the given power series:

$$\sum _{n=1}^{ \infty} \frac{(-1)^n x^{5n+2}}{5n+2}$$

Through the ratio test, I can get it down to $$ \frac{(-1)^n+1 x^{5(n+1)+2}}{5(n+1)+2} /\frac{(-1)^n x^{5n+2}}{5n+2},$$ but then I am stuck.

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    What have you tried? What do you know about how to find the radius of convergence of a power series?2012-11-08
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    "Ctrl", unlike other sites, we typically require *some* effort on the part of the asker. Please edit your question to include your thoughts/attempts. You won't get better at math by having other people do the heavy lifting!2012-11-08

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