Chapter 6.2, Problem 102E

T] Evaluate the power series expansion ln(1 + x) = $(1+x)={\displaystyle \underset{n=1}{\overset{\infty }{\sum }}{(-1)}^{n-1}\frac{x^n}{n}}$ at x = 1 to show that In (2) is the sum of the alternating harmonic series. Use the alternating series test to determine how many terms of the sum are needed to estimate In (2) accurate to within 0.001, and find such an approximation.