seriesstrategies - Series Strategies and Tests for...

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Series Tests for Convergence, Page 1/3 Series Strategies and Tests for Convergence Test Name When to Use Details Known Series – Geometric When you recognize that the terms are a constant raised to some power ï ï î ï ï í ì > < å = 1 if diverges 1 if 1 to converges 0 r r r a r a n n Known Series – p series When you recognize that the terms are n 1 raised to a constant power. ï î ï í ì > å = 1 when diverges 1 when converges 1 1 p p n n p Limit test (“Bouncer” test) If you can easily see how the s ' n a behave as a sequence. If 0 lim n n a , the series diverges. If 0 lim = n n a , the test is inconclusive. Alternating Series Test When the series is alternating. Usually, you’ll see a n ) 1 ( , 1 ) 1 ( n , or 1 ) 1 ( + n . Sometimes you’ll see a ÷ ø ö ç è æ ± π 2 1 2n sin or a ) cos( n Given å n n b ) 1 (: IF: 1. 0 > n b for all n AND 2. n n b b > + 1 for all n AND 3. 0 lim = n n b THEN the series converges.
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seriesstrategies - Series Strategies and Tests for...

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