Determine whether the series:$\displaystyle \sum_{n=1}^\infty$ 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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Originally Posted by Angel Rox Determine whether the series:$\displaystyle \sum_{n=1}^\infty$ 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. $\displaystyle 25^{-(n+2)} \cdot 16^{n+1} = \frac{16^{n+1}}{25^{n+2}} = \frac{16}{25^2} \cdot \left( \frac{16}{25} \right)^n$. 2. Sum of an infinite geometric series.
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