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8.4 Comparison Test

# 8.4 Comparison Test - 8.4ComparisonTests 1 1 n >1 2 n =1 n...

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8.4 Comparison Tests Recall we proved that the Harmonic Series diverged because 1 n n = 1 > 1 + 1 2 n = 1 Comparison Test Let a n be a series with nonnegative terms. a. a n converges if there is a convergent series c n with a n ≤ c n for all n > N for some integer N. b. a n diverges if there is a divergent series of nonnegative terms d n with d n ≤ a n for all n > N for some integer N. Ex. sin n n 2 n = 1

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Ex. 1 n 3 n = 10 Ex. 5 2 + 3 n n = 1 Limit Comparison Test Suppose that a n > 0 and b n > 0 for all n ≥ N (N an integer) 1. If lim n →∞ a n b n = c > 0 then a n and b n both converge or both diverge. 2. If lim n →∞ a n b n = 0 and b n converges, then a n converges.

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8.4 Comparison Test - 8.4ComparisonTests 1 1 n >1 2 n =1 n...

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