Chapter 8.6, Problem 62E

a.

To determine

To sketch: The graph of the function $N\left(r\right)$ for the three alternating p-series ${\displaystyle \sum _{k=1}^{\infty }\frac{{\left(-1\right)}^{k+1}}{k^p}}$, for $p=1,2\text{ and 3}$ and compare the three graphs and discuss the rates of convergence of three series.

b.

To determine

To sketch: The graph of the function $N\left(r\right)$ for the series ${\displaystyle \sum _{k=1}^{\infty }\frac{{\left(-1\right)}^{k+1}}{k!}}$ and compare the rates of convergence of all four series.