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Evaluating an infinite series Write the Taylor series for
Chapter 8, Problem 47E(choose chapter or problem)
Evaluating an infinite series Write the Taylor series for f(x) = In (1 + x) about 0 and find the interval of convergence. Assume the Taylor series converges to f on the interval of convergence. Evaluate f(1) to find the value of \(\sum_{k=1}^{\infty} \frac{(-1)^{k+1}}{k}\) (the alternating harmonic series).
Questions & Answers
QUESTION:
Evaluating an infinite series Write the Taylor series for f(x) = In (1 + x) about 0 and find the interval of convergence. Assume the Taylor series converges to f on the interval of convergence. Evaluate f(1) to find the value of \(\sum_{k=1}^{\infty} \frac{(-1)^{k+1}}{k}\) (the alternating harmonic series).
ANSWER:Step 1 of 3
Given that
f(x) = 1n (1 + x) about 0
(the alternating harmonic series).