Evaluate the convergence of the series .

MATHEMATICS · Single correct · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series

Problem

Evaluate the convergence of the series ∑n=3∞7 n−3(n−2) 7 n\displaystyle \sum_{n=3}^{\infty} \frac{7^{\,n-3}}{(n-2)\,7^{\,n}}. (a) It converges by the Ratio Test since the common ratio is 17<1\dfrac{1}{7}<1. (b) It diverges because its terms do not approach zero. (c) It diverges because the series reduces to a constant multiple of the harmonic series. (d) It converges by comparison to a pp-series with p=2p=2.

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