Section10.3b-ConvergenceOfSeriesWithPositiveTerms

Suspectconvergencebut 1 1 2 n2 5 n

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Unformatted text preview: Test) 5 cos 2 n 3 n n 1 Example 4 1 n2 5 n 3 What to do? Suspect convergence, but 1 1 2 n2 5 n Limit Comparison Test Let {an} and {bn} be positive sequences. Assume that the following limit exists: an n b n L lim i) If L > 0, then converges if and only if converges. bn an ii) If L = ∞ and converges, then converges. bn an iii) If L = 0 and converges, then converges. an bn Return to Example 4 1 1 n2 5 n 3 Compare to 1 n2 1 2 n 2 5 lim n 1 lim n n n 2 5 1 n2 1 n2 2 Both series have positive terms. finite and not 0 is a convergent p‐series, p = 2 > 1 3 4 1 2 is convergent by LCT (Limit Comparison Test) n 3 n 5 5 Example 5 1 n...
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