A power series is given by Explain

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

Problem

A power series is given by ∑n=0∞cn (x−5)n.\displaystyle \sum_{n=0}^{\infty} c_n\,(x-5)^{n}. Explain, in one or two sentences, why replacing each coefficient cnc_n by ∣cn∣|c_n| does not affect the series’ radius of convergence.

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