A power series converges for

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

Problem

A power series ∑n=0∞bntn\displaystyle \sum_{n=0}^{\infty} b_n t^{n} converges for ∣t∣<2|t|<2. For what real values of xx does the series ∑n=0∞bn (3x−1)n\displaystyle \sum_{n=0}^{\infty} b_n\,(3x-1)^{n} converge? Give your answer as an open interval.

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