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For each of the following series, indicate whether the integral test can be used to determine its convergence not, and if not, why. Α. Σ n=1 cos(n) n² Can the integral test be used to test convergence? ○ A. no, because the terms in the series do not decrease in magnitude ● B. no, because the terms in the series are not all positive for n ≥ c, for some c > 0 ○ C. no, because the series is not a geometric series ○ D. no, because the terms in the series are not recursively defined ○ E. no, because the terms in the series are not defined for all n OF yes B. ☎ In(1.3n) n=1 Can the integral test be used to test convergence? ○ A. no, because the terms in the series do not decrease in magnitude ● B. no, because the terms in the series are not all positive for n ≥ c, for some c > 0 ○ C. no, because the series is not a geometric series ○ D. no, because the terms in the series are not recursively defined ○ E. no, because the terms in the series are not defined for all n

For each of the following series, indicate whether the integral test can be used to determine its convergence not, and if not, why. Α. Σ n=1 cos(n) n² Can the integral test be used to test convergence? ○ A. no, because the terms in the series do not decrease in magnitude ● B. no, because the terms in the series are not all positive for n ≥ c, for some c > 0 ○ C. no, because the series is not a geometric series ○ D. no, because the terms in the series are not recursively defined ○ E. no, because the terms in the series are not defined for all n OF yes B. ☎ In(1.3n) n=1 Can the integral test be used to test convergence? ○ A. no, because the terms in the series do not decrease in magnitude ● B. no, because the terms in the series are not all positive for n ≥ c, for some c > 0 ○ C. no, because the series is not a geometric series ○ D. no, because the terms in the series are not recursively defined ○ E. no, because the terms in the series are not defined for all n

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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For each of the following series, indicate whether the integral test can be used to determine its convergence or not, and if not, why. A. cos(n) n=1 Can the integral test be used to test convergence? ○ A. no, because the terms in the series do not decrease in magnitude B. no, because the terms in the series are not all positive for n ≥ c, for some c > 0 ○ C. no, because the series is not a geometric series ○ D. no, because the terms in the series are not recursively defined E. no, because the terms in the series are not defined for all n F. yes ∞ B. ☎ ln(1.3n) Σ n=1 Can the integral test be used to test convergence? ○A. no, because the terms in the series do not decrease in magnitude B. no, because the terms in the series are not all positive for n ≥ c, for some c > 0 C. no, because the series is not a geometric series ○ D. no, because the terms in the series are not recursively defined E. no, because the terms in the series are not defined for all n OF. yes
Transcribed Image Text:For each of the following series, indicate whether the integral test can be used to determine its convergence or not, and if not, why. A. cos(n) n=1 Can the integral test be used to test convergence? ○ A. no, because the terms in the series do not decrease in magnitude B. no, because the terms in the series are not all positive for n ≥ c, for some c > 0 ○ C. no, because the series is not a geometric series ○ D. no, because the terms in the series are not recursively defined E. no, because the terms in the series are not defined for all n F. yes ∞ B. ☎ ln(1.3n) Σ n=1 Can the integral test be used to test convergence? ○A. no, because the terms in the series do not decrease in magnitude B. no, because the terms in the series are not all positive for n ≥ c, for some c > 0 C. no, because the series is not a geometric series ○ D. no, because the terms in the series are not recursively defined E. no, because the terms in the series are not defined for all n OF. yes
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