# Shared Flashcard Set

## Details

Calc 2 Series Tests
Results of Convergence/Divergence Tests of Series
10
Mathematics
07/21/2009

Term
 Test for Divergence
Definition
 IF lim n->oo An does not exist or != 0, series An is divergent
Term
 Integral Test
Definition
 IF continuous, positive, decreasing on [1,oo), IF f(x) converges so does series An, if not ""
Term
 Comparison Test
Definition
 IF series An and Bn are positive, if Bn is convergent and > An, An is convergent. If Bn is divergent and Bn < An, An is divergent.
Term
 Limit Comparison
Definition
 Series An and Bn positive, if lim n->oo An / Bn = C where C is finite and > 0, both converge or diverge
Term
 Alternating Series
Definition
 If decreasing and lim n->oo Bn = 0, converges.
Term
 Ratio Test
Definition
 If lim n->oo An+1/An = L, L < 1 Series An is abs. convergent. L > 1 || L = oo series is divergent. L = 1 inconclusive.
Term
 Root Test
Definition
 IF lim n->oo (An)^1/n = L, L < 1 Series An is abs. convergent. L > 1 || L = oo series is divergent. L = 1 inconclusive.
Term
 Geometric Series
Definition
 ar^n-1convergent if |r|<1, sum = a/1-rdivergent if |r|>=1
Term
 Harmonic
Definition
 1/n always diverges
Term
 P-Series
Definition
 1/n^p convergent if p>1 else divergent
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