post 10.

soooo, we got a big test tomorrow in calc. so let's go over what is gonna be on that!

p-series:
used whenever you have n^#.
if # is 1 it converges.

geometric series:
used whenever you have #^n
if abs.value of # <> 1, continue on to testing..
you would divide original by what you compared it to. then take the limit as n goes to infinty of that. & if you get # > 1, it diverges. if not, it is inconclusive.

nth term test:
you use this when you don't exactly know what else to do & you are just testing.
take the lim as x goes to infinity.
if you get anything besides 0, it diverges. if you get 0, it's inconclusive.

integral test:
this is used whenever you have absolutely nothing else to do. you take the integral from n to infinity
if you get infinity, it diverges. if you get a number, it converges.

alternating series test:
used whenever you have -1 or -2 raised to n.
you take out that portion of the problem, then continue on. but if you have -2, you just take out the negative.
after taking it out, you take the limit as n goes to infinity.
if you get anything besides 0, it diverges. if you get 0, continue on & add one to every n.
then compare to the original after you took out the -# ^ n by doing (n+1 equation) ^ if above is true, then converges. if false, then diverges.

sum of geometric series:
first term/1-r

sum of nongeometric series:
n(t1 + tn)/2

ratio test:
use if it tells you to.. pretty much.
add one to each n. then divide <-- that by the original. then take lim as n goes to inifinty.
if you get # <> 1 or infinity, it diverges.
(also you use this if you have a factorial!)

NOW for what I don't understand...
-direct comparison test
-limit comparison test
-absolute convergence
-conditional convergence