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### 14 Cards in this Set

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 p series 1/n to p power if p>1 con if p<1 div basic comparison test sum of Bn con AND An is less than or equal to Bn then An con sum of Bn div AND An is greater than or equal to Bn then An div limit comparision test if An is given and Bn is reference series limit of An/Bn=C and C>0, then both series con or both div limit An/Bn=0 and sum of Bn con, then An con limt of An/Bn= infinity and sum of Bn div, then An div alternating series test sum of -1 to n-1 power as 1 to infinity is an alternating series if limit of An =0 AND An+1 < An for all n, then the given series converges another way to show decreasing, f'x <0 integral test if f is cont., +, decreasing function on [1,infinity) then if the sigma series is con iff the improper integral is con. therefore if integral is con, then the sigma series is con. if integral is div, then sigma is div absolutely con if series of abs values sigma An is con, then it is called absolutely con conditionally con if the sigma An is con, but is not absolutely con. if sigma An is absolutely con then it is con ratio test the limit of An+1/An =L L<1 then An series is absolutely con L>1 or =infinity, then An series is divergent root test nth root of abs value of An =L L <1 then series of An is absolutely con L>1, then the series of An is div power series series converges only when x=a series converges for all x there is a + # R such that the series converges if abs value of x-a R power series when -1 or = to 1, the series is div root test used when An->Bn to the n power ratio test when constant is to the nth power or involves n!