Chapter 9.4, Problem 53E

Evaluating an infinite series Write the Taylor series for f(x) = ln (1 + x) about 0 and find its interval of convergence. Assume the Taylor series converges to f on the interval of convergence. Evaluate f(1) to find the value of ${\displaystyle \underset{k=1}{\overset{\infty }{\sum }}\frac{{(-1)}^{k+1}}{k}}$ (the alternating harmonic series).