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Calculate the sum of the geometric series 1 + 1/5^2 + 1/5^4 + .... Express your answer as a common fraction.

 Dec 31, 2021
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\(1+\frac{1}{5^2}+\frac{1}{5^4}+ \mbox{ } ... \mbox{ } = \displaystyle\sum_{n=1}^{\infty} 5^{-2(-1+n)} = \frac{25}{24}\) .

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 Dec 31, 2021

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