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I'm stuck with my homework:

Find both the radius and interval of convergence for the given series. Also, determine the values of $x$ for which the series converges absolutely and those for which the series converges conditionally.

(a) $\displaystyle\sum_{k=1}^{\infty}k(x-2)^k$

(b) $\displaystyle\sum_{k=1}^{\infty}\frac{1}{k}\left(\frac{x}{2}\right)^k$

(c) $\displaystyle\sum_{k=1}^{\infty}k\left(-\frac{1}{3}\right)^k(x-2)^k$

(d) $\displaystyle\sum_{k=1}^{\infty}\frac{2^kk!}{k^k}x^k$

(e) $\displaystyle\sum_{k=1}^{\infty}\frac{k}{3^{2k-1}}(x-1)^{2k}$

  • 4
    Where are you stuck?2011-12-12
  • 0
    I think I just need an example, I don't now how to do this correctly.2011-12-12
  • 0
    Here are some examples for the ratio test: http://en.wikipedia.org/wiki/Ratio_test#Examples2011-12-12

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