Hi does anyone know how Abel's test and Leibnitz's test( also called the 'alternating series test' for convergence) are related? Is the alternating series test sometimes called Abel's test? The alternating series test states:
Let $\{a_{n}\}$ be a non-negative sequence of numbers, which are monotone decreasing to $0$. Then the series $\sum(-1)^{n}a_{n}$ converges, and $$\left\vert\sum_{n=1}^{\infty}(-1)^{n}a_{n}\right\vert \leq a_{1}$$
Thanks