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Nth Term Test

If Limit as K approaches infinity, then the Series of K Diverges.

Alternating Series Test

If An is positive, the series ∑(-1)An converges if & only if..

Geometric Series Test

general term = a₁r^n, converges if -1 < r < 1

P-Series Test

general term = 1/n^p, converges if p > 1

Integral Test

take integral and evaluate, if it goes to a number it is convergent, if there is ∞in it, its divergent

Root Test

if limit as n nears infinity of the nth root of a sub n is less than 1, the series CONVERGES; and if the limit is greater than 1 or infinity, the series DIVERGES

Comparison Test

after comparing remember to take the limit as n→∞ of an/bn and for convergence it must lie on the interval 0<L<∞

Ratio Test

limit as n→∞ of an+1/an

nth-term

Diverges: lim n→∞ an ≠ 0

geometric series

sum of the terms of an arithmetic sequence

telescoping series

Converges: lim→∞ bn = L

P-Series

Sum where 1/(n^p) converges if and only if p > 1

integral

(works if f(x) is continuous, positive, decreasing)

root

A root of a polynomial in one variable is a value of the variable for which the polynomial is equal 0.

ratio

A comparison of two quantities, also know as fancy word for fraction.

0<an≤bn

direct comparison

limit comparison

Series converges if lim (as n approaches infinity) a{n}/ b{n}= L>0 and