Convergence/Divergence Conditions and Outcomes

Convergence with Ratio Test happens when…

Divergence with Ratio Test happens when…

Ratio test is inconclusive if…

An ALTERNATING SERIES will converge if:

If with an ALTERNATING SERIES…

Nth TERM TEST

Nth TERM TEST is inconclusive when…

DIRECT COMPARSION TEST conditions show convergence when…

DIRECT COMPARSION TEST conditions show divergence when…

Limit Comparison Test shows…

Harmonic Series

HARMONIC SERIES will always

Will always diverge.

Conditions for INTEGRAL TEST

The sum of a convergent infinite GEOMETRIC SERIES is…

A P-SERIES is of the form….

A P-SERIES converges if….

A P-SERIES diverges if….

An infinite GEOMETRIC SERIES is of the form…

An infinite GEOMETRIC SERIES converges if…

An infinite GEOMETRIC SERIES diverges if…

To use the DIRECT COMPARSION TEST you must have the following condition…

a_n >0 and b_n > 0 for all n

To use the LIMIT COMPARSION TEST you must have the following condition…

are ALTERNATING SERIES