Evaluating an infinite series Write the Taylor series for

Chapter 8, Problem 47E

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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).

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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).

 

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