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Tutorialreview - Review for MATH 262 series tests error...

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1/30/2010 1 Review for MATH 262 series tests error approximation power series Sequences Easy stuff right...? Series 0 n n a N th term test (Divergence Test) If , series DIVERGES If limit = 0, test INCONCLUSIVE 0 lim n n a Telescoping Series Examples: Expand, cancel terms, and apply limit to the remaining n th terms Use partial fraction decomposition Geometric Series If |x|< 1, Series CONVERGES And Sum = Note: formula works for starting index at n=0 !! Else, Series DIVERGES 0 n n ax x a 1
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1/30/2010 2 P-Series If P>1, Series CONVERGES If P=1, Series DIVERGES If P<1, Series DIVERGES p n 1 Integral Test Is the series a POSITIVE & DECREASING series? If yes, If the improper integral of a FUNCTION which contains all the points of the sequence a n has a limit L: L < ∞ Series CONVERGES L = Series DIVERGES Comparison Test {a n} , {b n }are POSITIVE sequences If and CONVERGES Series CONVERGES also If and DIVERGES Series DIVERGES also n b n b n n a b 0 n n b a 0 Limit Comparison Test Choose a series bn for which you know the behavior
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