Summary of Convergence Tests

Geometric series

A series of the form ∑ar^k converges if and only if |r|<1. The infinite sum of such a series i S = a/1-r where a is the f

The Divergence Test

A series ∑a_k diverges if limit as k goes to infinity of a_k ≠ 0

P Series

A series of the form ∑ 1/k^p. Converges if and only p>1

Harmonic series

The special case of a p-series in which p =1 diverges

Alternating Series Test

the series (-1)^k a_k converges if lim k approaches infintiy = 0 and its decreasing

The ratio test

<1 converges

>1 diverges

=1 incuclusive