A power series has radius of convergence

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

Problem

A power series ∑n=0∞an(x−1)n\sum_{n=0}^{\infty} a_n (x-1)^n has radius of convergence RR. A new series is formed by multiplying every coefficient by 77, giving ∑n=0∞7an(x−1)n\sum_{n=0}^{\infty} 7a_n (x-1)^n. What is the radius of convergence of the new series?

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