Ratio Test:

When does it converge & diverge & is inconclusive.

if the lim n-> ∞ < 1 then the series converges

if the lim n-> ∞ < 1 then the series Diverges

if the lim n-> ∞ == 1 then the series is inconclusive

P - Series:

When does a series converge, and diverge.

The Series converges if P> 1, diverges if P <= 1.

Divergence Test / (nth term divergence test):

When does it converge & diverge & is inconclusive.

of the lim n-> 0, then the test is inconclusive.

Direct Comparison Test:

When does a series converge, and diverge.

• If 0≤an≤bn (bn converges then an also converges)
• If an≥bn≥0 (if bn diverges then an also diverges)

Limit Comparison Test:

What is the formula for the test?

What does L have to be to converge?

What does L have to be to diverge?

If L is a finite positive number (0 < L < ∞)

Both series (an) and (bn) either converge or diverge)

If L = 0 and Bn converges

An also converges

if L = ∞ and Bn Diverges

then An also diverges

Alternating Series Test:

When does it converge, and diverge?

When Lim n->oo an = 0

Geometric Series:

What is the series look like? when does it converge and diverge?

If |R| >= 1 then it diverges, |R| < Converges.

Integral Test:

What does f(x) need to be to converge.

• Continuous,
• Positive,
• Decreasing for x≥1 then the series and the corresponding improper integral either both converge or both diverge.