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