Convergence/Divergence Tests (AP Calculus BC) Flashcards

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