MediumPower & Taylor series

Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §10.5 Power Series, #21 · Calculus · Power & Taylor series

Find … in Problem 20 and show that the series converges to…

17–24 are about remainders and are about binomials.

Find $R_{n}$ in Problem 20 and show that the series converges to the function at $x = \frac{1}{2}$ (prove that $R_{n} \to 0$ ).

This exercise builds on another exercise in its source book, which isn't shown here.

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §10.5 Power Series, #21

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