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Answer:

[tex] \frac{1}{ 2^{1} } + \frac{1}{ {3}^{2} } + \frac{1}{ {4}^{3} } + \frac{1}{ {5}^{4} } + ... \\ \frac{1}{2} + \frac{1}{9} + \frac{1}{64} + \frac{1}{625} + ... \\ = \frac{226201}{360000} \\ = 0.6283..[/tex]