For , the series converges to a function . Determine an explicit power-series…

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

Problem

For ∣x−2∣<1|x-2|<1, the series ∑n=0∞n(x−2)n\displaystyle \sum_{n=0}^{\infty} n(x-2)^{n} converges to a function g(x)g(x). Determine an explicit power-series expression for an antiderivative of gg centered at x=2x=2, including the constant of integration CC.

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