For , the power series converges…

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

Problem

For x>0x>0, the power series 1−x23!+x45!−x67!+⋯+(−1)nx2n(2n+1)!+⋯1-\frac{x^2}{3!}+\frac{x^4}{5!}-\frac{x^6}{7!}+\cdots+(-1)^n\frac{x^{2n}}{(2n+1)!}+\cdots converges to

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