For a real parameter

MATHEMATICS · Subjective · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series

Problem

For a real parameter pp, let an=nnp+1a_n=\dfrac{n}{n^{p}+1}. For which values of pp does the series ∑n=1∞an\displaystyle\sum_{n=1}^{\infty} a_n diverge by the nnth term test?

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