# Alternating Series

## Alternating Series Test

The alternating series  converges provided  1) the terms of the series are monotonically decreasing  2)

## Remainder in Alternating Series

Let be a convergent alternating series with terms that are non increasing magnitude. Let be the remainder in approximating the value of the series by the sum of its first n terms. Then . In other words, the remainder is less than or ewaul to the magnitude of the first neglected term.

## Absolute and Coditional Convergence

If converges, then converges absolutely. If diverges and converges, then converges conditionally.