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

Let

be an infinite series with non-negative term sand let

the series converges 2)

the series diverges 3)

the test is inconclusive

Let

and

be series with positive terms. 1) If

diverges

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