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Convergence of series

  1. Jan 23, 2005 #1
    Hi all,

    I have this series:

    \sum_{n = 1}^{+\infty} \tan \left( \frac{\pi}{4^{n}} \right) . \sin 2^{n}

    I have to find out whether it converges or not, but I don't know how should I start. The only idea coming to my mind is to use Abel-Dirichlet's rule for convergence, but I don't know how to prove that sin has limited partial sums. Then I could use the rule I hope.

    Or is there any other and more clever way how to prove the convergence?

    Thank you.
  2. jcsd
  3. Jan 23, 2005 #2
    \sum_{n = 1}^{+\infty} \tan \left( \frac{\pi}{4^{n}} \right) \cdot \sin 2^{n} < \sum_{n = 1}^{+\infty} \tan \left( \frac{\pi}{4^{n}} \right)
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