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1 Let an = 9 √n + ln (n) and bn = Calculate the following limit. (Give an exact answer. Use symbolic notation and fractions where needed. Enter DNE if the limit does not exist.) an lim = n→∞ bn ∞ Determine the convergence of Σ an. n=1 ∞ Σan diverges by the Limit Comparison Test since Σb, diverges and lim is infinite. n→∞ bn n=1 n=1 an diverges by the Limit Comparison Test since bn diverges and lim an n→∞o bn exists and is finite. n=1 n=1 ∞ ∞0 an converges by the Limit Comparison Test since bn converges and lim does not exist. n=1 n=1 ∞0 ∞ Σ an converges by the Limit Comparison Test since bn converges. n=1 n=1 Ο Ο Ο an n→∞ bn

1 Let an = 9 √n + ln (n) and bn = Calculate the following limit. (Give an exact answer. Use symbolic notation and fractions where needed. Enter DNE if the limit does not exist.) an lim = n→∞ bn ∞ Determine the convergence of Σ an. n=1 ∞ Σan diverges by the Limit Comparison Test since Σb, diverges and lim is infinite. n→∞ bn n=1 n=1 an diverges by the Limit Comparison Test since bn diverges and lim an n→∞o bn exists and is finite. n=1 n=1 ∞ ∞0 an converges by the Limit Comparison Test since bn converges and lim does not exist. n=1 n=1 ∞0 ∞ Σ an converges by the Limit Comparison Test since bn converges. n=1 n=1 Ο Ο Ο an n→∞ bn

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section: Chapter Questions
Problem 63RE
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1 Let an = 9 √n + In (n) and bn Calculate the following limit. √n (Give an exact answer. Use symbolic notation and fractions where needed. Enter DNE if the limit does not exist.) an lim = n→∞ bn ∞ Determine the convergence of Σ an. n=1 ∞ an diverges by the Limit Comparison Test since bn diverges and lim an is infinite. n→∞ bn n=1 ∞ Σan diverges by the Limit Comparison Test since bn diverges and lim an n→∞ bn exists and is finite. n=1 an converges by the Limit Comparison Test since bn converges and lim does not exist. an bn n→∞ n=1 n= ∞ ∞ Σ an converges by the Limit Comparison Test since b, converges. n=1 n=1 =
Transcribed Image Text:1 Let an = 9 √n + In (n) and bn Calculate the following limit. √n (Give an exact answer. Use symbolic notation and fractions where needed. Enter DNE if the limit does not exist.) an lim = n→∞ bn ∞ Determine the convergence of Σ an. n=1 ∞ an diverges by the Limit Comparison Test since bn diverges and lim an is infinite. n→∞ bn n=1 ∞ Σan diverges by the Limit Comparison Test since bn diverges and lim an n→∞ bn exists and is finite. n=1 an converges by the Limit Comparison Test since bn converges and lim does not exist. an bn n→∞ n=1 n= ∞ ∞ Σ an converges by the Limit Comparison Test since b, converges. n=1 n=1 =
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