# The Root, Ratio, and Integral Tests

Topic:
Root

## Ratio Test

Let be an infinite series with positive terms and let . 1) the series converges 2) the series diverges 3) r=1 the test is inconlusive

## Root Test

Let be an infinite series with non-negative term sand let 1) the series converges 2) the series diverges 3) the test is inconclusive

## Comparison Test

Let and be series with positive terms. 1) If diverges

## Limit Comparison Test

Let and be series with positive terms and let !) If L is a finite positive real number, then and either both converge or both diverge 2) If L=0, and converges, then converges 3) if and diverges, then diverges