Chapter 8.1, Problem 118PE

Using calculus, we can show that the series ${\displaystyle \underset{k=1}{\overset{n}{\sum }}{\left(-1\right)}^{k-1}\frac{{\left(0.5\right)}^k}{k}}$ approaches in 1.5 as n approaches infinity. Investigate this statement by evaluating the sum for $n=10$ and $n=50$.