**Divergence or nth term test**

Series:

Convergence or Divergence: Diverges if

Comments: Nothing can be said if

**Geometric Series Test**

Series:

Convergence or Divergence:

* converge and have sum if | r | <1.

* diverges if | r | 1

Comments: Useful for comparison tests

**P-series test**

Series:

Convergence or Divergence:

* converge if p> 1

* diverges if p 1

Comments: Useful for comparison tests

**Limit comparison test**

Series: and , a_{no} > 0, b_{no} > 0

Convergence or Divergence:

* If , , then both series converge or both diverge.

* If and converge then converge.

* If and diverges then diverges.

Comments: The Comparison Series , is usually a geometric series or a p-series.

To find b_{no}, only the terms of the_{no} that have the greatest effect.

**Leibniz test**

Series: ALTERNATE

, a_{no }> 0

Convergence or Divergence:

Converge if:

*

* The series of the modules is decreasing.

Comments: Applicable **only **to alternating series. If the first item is false, the divergence test applies.