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Math Help - Converging or Diverging...??

  1. #1
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    Red face Converging or Diverging...??

    Determine whether the series: \sum_{n=1}^\infty 25^-n+2 . 16^n+1converges or diverges. If it converges then find its sum


    Can I have some hints in solving this question..
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  2. #2
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    Quote Originally Posted by Angel Rox View Post
    Determine whether the series: \sum_{n=1}^\infty 25^-n+2 . 16^n+1converges or diverges. If it converges then find its sum


    Can I have some hints in solving this question..
    Two hints:

    1. 25^{-(n+2)} \cdot 16^{n+1} = \frac{16^{n+1}}{25^{n+2}} = \frac{16}{25^2} \cdot \left( \frac{16}{25} \right)^n.

    2. Sum of an infinite geometric series.
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