Mathematics

Mathematics

Problem

Let pp be a real number. Consider the series ∑n=1∞p n1+p n\displaystyle\sum_{n=1}^{\infty}\frac{p^{\,n}}{1+p^{\,n}}. For which values of pp must this series diverge? a) ∣p∣>1|p|>1 b) ∣p∣≥1|p|\ge 1 c) ∣p∣>1  or  p=1|p|>1\,\text{ or }\,p=1 d) p=1p=1

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