Leibniz criterion

Leibniz criterion

Let $(a_k{)}_{k\in \mathbb{N}}$ be a monotone null sequence. Then, the series

$$\sum _{k=1}^{\infty }(-1{)}^{k+1}{a}_k\text{converges}$$

Proof:

Todo

Does $\sum \frac{(-1{)}^{k+1}}{k}$ converge?