## Calculus (3rd Edition)

Given $$\sum_{n=1}^{\infty} \frac{(-1)^{n-1}}{\sqrt{n}+\sqrt{n+1}}$$ This is an alternating series. Consider $a_{n}=\dfrac{1}{\sqrt{n}+\sqrt{n+1}}$, since $\{a_n \}$ is a decreasing sequence and \begin{align*} \lim _{n \rightarrow \infty} a_{n}&=\lim _{n \rightarrow \infty} \dfrac{1}{\sqrt{n}+\sqrt{n+1}}\\ &=0 \end{align*} Then by using the Leibniz Test, the given series converges.