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| 1323758674 | test for divergence | diverges if lim(n→∞)≠0 | 0 | |
| 1323758675 | geometric series | converges when |r|<1 diverges when |r|≥1 | 1 | |
| 1323758676 | p-series | converges when p>1
diverges when 0| 2 | | |
| 1323758677 | integral test | converges if 1∫∞f(x)dx converges diverges if 1∫∞f(x)dx diverges Basically, if integral converges/diverges, then series will do the same | 3 | |
| 1323758678 | direct comparison test | converges when an≤bn and bn converges diverges when an≥bn and bn diverges | 4 | |
| 1323758679 | limit comparison test | 1.) if lim(n→∞) an/cn = 0 and cn converges, so does an 2.) if lim(n→∞) an/cn = ∞ and cn diverges, so does an 3.) if lim(n→∞) an/cn = any other real number, then both series have same status (both converge/diverge) | 5 | |
| 1323758680 | ratio test | converges if L<1 diverges if L>1 inconclusive if L = 1 (try another test!) | 6 | |
| 1323758681 | alternating series test | converges if dec and lim(n→∞)=0 | 7 | |
| 1323758682 | absolute convergence | if ∑|an| converges then ∑an converges | 8 | |
| 1327246396 | nth term test | 1.) if lim(n→∞) an = ∞ or any nonzero #, then the terms are inc in value, and series diverges 2.) if lim(n→∞) an = 0, inconclusive (try a different test!) | 9 |
