# The Divergence and Integral Tests

## Theorem 8.8 Divergence Test

If convergences, then   If the limit does not equal 0, then the series diverges.

## Theorem 8.9 The HarmonicSeries

The Harmonic Series diverges even though the terms approach zero

## Theorem 8.10 Integral Test

Suppose f is a continuous, positive, and decreasing function for , and let for k= 1, 2, 3, 4.... Then and either both converge or both diverge. In the case of convergence, the value of the integral is not equal to the value of the series

## Theorem 8.11 Convergence of p-Series

The p-series converges for and diverges for

## Properties of Convergent Series

Suppose converges to A and converges to b. Then A) B)