Answer
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Work Step by Step
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.
