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Convergence and divergence of series

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1. If a and b are positive integers then show that
sum (n=1 to infinity) (1/(an+b)^p) converges for p greater than 1 and diverges for p less than or equal to one.

2. Let a be greater than zero. show that the series
sum (n=1 to infinity)(1/(1+a^n)) is divergent if a is greater than zero or less than or equal to one, and is convergent for a greater than 1.

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Solution Summary

Sonvergence and divergence of two series depending on parameters are establieshed. The solutions are in a PDF file.

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