# The Root, Ratio, and Integral Tests

## 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

## Relating the Ratio Test to Geometric Series

## Comparison Test

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