EXAMPLE 5 Test the convergence of the series n! n = 1 SOLUTION Since the terms a, = n"/n! are positive, we don't need the absolute value signs. 3n +1 - (n + 1)n + 1 n! (n + 1)! )(n + 1)" n! (n + 1)n! - (*:)" - (1 • ±) -[ + 1 = as n → 00 Since e > 1, the given series is --Select-- v by the Ratio Test.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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n"
EXAMPLE 5 Test the convergence of the series
n!
n = 1
SOLUTION Since the terms a, = n"/n! are positive, we don't need the absolute value signs.
(n + 1)n + 1
(n + 1)!
an +1
n!
)(n + 1)"
n!
(n + 1)n!
- () -
n + 1
1
1 +
as n → co
n
Since e > 1, the given series is -Select- v by the Ratio Test.
Transcribed Image Text:n" EXAMPLE 5 Test the convergence of the series n! n = 1 SOLUTION Since the terms a, = n"/n! are positive, we don't need the absolute value signs. (n + 1)n + 1 (n + 1)! an +1 n! )(n + 1)" n! (n + 1)n! - () - n + 1 1 1 + as n → co n Since e > 1, the given series is -Select- v by the Ratio Test.
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