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Math Help - Series - convergent or divergent?

  1. #1
    Newbie Marbel's Avatar
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    Series - convergent or divergent?

    Determine whether the following series converges or diverges
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  2. #2
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    \sqrt{2}=2cos\frac{\pi}{4}, we see that a_n=\sqrt{2-2cos\frac{\pi}{2^n}}=\sqrt{4sin^2\frac{\pi}{2^{n+1  }}}=2sin\frac{\pi}{2^{n+1}}. then \sum\limits^{\infty}_{n=1}\frac{\pi}{2^n} converges and 2sin\frac{\pi}{2^{n+1}}<\frac{\pi}{2^n} so your series is convergent
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