Consider the infinite series

MATHEMATICS · Single correct · A Level · Mathematics · Sequences and series · Sequences and series

Problem

Consider the infinite series ∑n=0∞(−1)n+143n\displaystyle \sum_{n=0}^{\infty}(-1)^{n+1}\dfrac{4}{3^{n}}. When the series is written in the standard geometric form ∑n=0∞arn\sum_{n=0}^{\infty} ar^{n}, which of the following is the common ratio rr? (a) −43-\dfrac43 (b) \dfrac13 (c) −13-\dfrac13 (d) \dfrac43

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