## Definition 4.1.2: Series, Partial Sums, and Convergence

Let

*{a*be an infinite sequence._{n}}- The formal expression
is called an (infinite)
**series**. - For
*N = 1, 2, 3, ...*the expression*S*is called the_{N}=**N-th partial sum**of the series. - If
*lim S*exists and is finite, the series is said to_{N}**converge**. - If
*lim S*does not exist or is infinite, the series is said to_{N}**diverge**.