Determine whether the infinite series converges

MATHEMATICS · Subjective · A Level · Mathematics · Sequences and series · Sequences and series

Problem

Determine whether the infinite series ∑n=1∞5⋅2 n−13 n\displaystyle \sum_{n=1}^{\infty} \frac{5\cdot 2^{\,n-1}}{3^{\,n}} converges, and if it does, find its sum in simplest rational form.

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