Q2 e and f (using one of these : nth term test, direct comparison test, limit comparison test, ratio test, integral test or root test ) Q3 all utions to each of these problems on a seperate sheet of paper.1. Consider the seriesn=1In(n)n2(a) Try using the Limit Comparison Test with b(b) Try using the Limit Comparison Test with b1=12211Is the test conclusive? Explain your answer.Ba=. Is the test conclusive? Explain your answer.(c) Try using the Limit Comparison Test with bn1=n3/2-Is the test conclusive? Explain youranswer.2. For each of the following series determine if they converge or diverge. You may use any test we havecovered so far.(a)3+ cos(n!)玩n=1(b)²sin*(3/2)n=1(c) (-1)";n=1(3n)!(n!)362n+1(d) sin (+)(e)(f)n=2n=3n=0√n²-4m³ +In(n)2.5...(3n+2)2nn!(The expression in the numerator is called a running product. It is basically a factorial that skipsnumbers rather than multiplying every number together. This one starts at 2 and skips by 3 eachtime. So for instance, if n was 4 it would be 2.5.8.11.14.)3. Let an and bn be two sequences of positive numbers such that bn diverges.(a) If limAn+1(b) If limAn(c) If lim ann7x(d) If lim va8012==112'ེ2'=112'does an converge or diverge and what test justifies your conclusion?does an converge or diverge and what test justifies your conclusion?does an converge or diverge and what test justifies your conclusion?2'does an converge or diverge and what test justifies your conclusion?

2. For each of the following series determine if they converge or diverge. You may use any test we have covered so far. (a) 3+ cos(n!) n=1 玩 (b) Σn sin*(n3/2) n=1 (c) (-1) (3n)! (n!)362n+1 n=1 (d) sin (+) n=2 ∞ (0) Σ n=3 √n2-4 n3+ In(n) (f) 2- Σ n=0 2.5...(3n+2) 2nn! (The expression in the numerator is called a running product It is basically a factorial that skins

2. For each of the following series determine if they converge or diverge. You may use any test we have covered so far. (a) 3+ cos(n!) n=1 玩 (b) Σn sin*(n3/2) n=1 (c) (-1) (3n)! (n!)362n+1 n=1 (d) sin (+) n=2 ∞ (0) Σ n=3 √n2-4 n3+ In(n) (f) 2- Σ n=0 2.5...(3n+2) 2nn! (The expression in the numerator is called a running product It is basically a factorial that skins

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section5.6: Exponential And Logarithmic Equations

Problem 64E

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