*2. (a) If you have successfully solved examples (xix) and (xx) from Problem 1, it should be clear that 2 a"n!/n" converges for a < e and diverges for a > e. For a = e the ratio test fails; show that e"n!/n" actually diverges, by using Problem 21-13. (b) Decide when 2 n" /a"n! converges, again resorting to Problem 21-13 when the ratio test fails.
*2. (a) If you have successfully solved examples (xix) and (xx) from Problem 1, it should be clear that 2 a"n!/n" converges for a < e and diverges for a > e. For a = e the ratio test fails; show that e"n!/n" actually diverges, by using Problem 21-13. (b) Decide when 2 n" /a"n! converges, again resorting to Problem 21-13 when the ratio test fails.
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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Please solve both parts
Transcribed Image Text:*2. (a) If you have successfully solved examples (xix) and (xx) from
Problem 1, it should be clear that 2 a"n!/n" converges for a < e
and diverges for a > e. For a = e the ratio test fails; show that
e"n!/n" actually diverges, by using Problem 21-13.
(b) Decide when 2 n"/a"n! converges, again resorting to Problem
21-13 when the ratio test fails.
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