## Calculus 10th Edition

See Definitions of Convergent and Divergent Series (page 595). For the infinite series $\displaystyle \sum_{n=1}^{\infty}a_{n}$, the nth partial sum is $S_{n}=a_{1}+a_{2}+\cdot \cdot +a_{n}$. If the sequence of partial sums $\{S_{n}\}$ converges to $S$, then the series $\displaystyle \sum_{n=1}^{\infty}a_{n}$ converges. The limit $S$ is called the sum of the series. $S=a_{1}+a_{2}+... +a_{n}+...,\displaystyle \qquad S=\sum_{n=1}^{\infty}a_{n}$ If $\{S_{n}\}$ diverges, then the series diverges.