Transcription of Tests for Convergence of Series 1) Use the comparison test ...
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Tests for Convergence of Series 1) Use the comparison test ...
Tests for Convergence of Series1) Use the comparison test to confirm the statements in the following n=41ndiverges, so n=41n : Letan= 1/(n 3), forn 4. Sincen 3< n, we have 1/(n 3)>1/n, soan> harmonic Series n=41ndiverges, so the comparison test tells us that the Series n=41n 3also n=11n2converges, so n=11n2+ : Letan= 1/(n2+ 2). Sincen2+ 2> n2, we have 1/(n2+ 2)<1/n2, so0< an< Series n=11n2converges, so the comparison test tells us that the Series n=11n2+2also n=11n2converges, so n=1e : Letan=e n/n2. Sincee n<1, forn 1,we havee nn2<1n2, so0< an< Series n=11n2converges, so the comparison test tells us that the Series n=1e nn2also ) Use the comparison test to determine whether the Series in the following exercises n=113n+1 Answer: Letan= 1/(3n+ 1).
1 n=0 2n 3+1 diverges. 4) Use the integral test to decide whether the following series converge or diverge. 1. X1 n=1 1 n3 Answer: We use the integral test with f(x) = 1=x3 to determine whether this series converges or diverges. We determine whether the corresponding improper integral Z 1 1 1 x3
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