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Convergence of Series with Factorials
Worksheet
Grade Level
Calculus II
CAL2.130 Convergence of Series with Factorials
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Consider the series \(\sum_{n=1}
\infty
(-1)
n
\frac{\sqrt n\,n!}{(n+1)!}\). Which test and conclusion are correct?
A
Ratio Test on absolute values: \(L = 0\); the series converges absolutely.
B
Alternating Series Test: the series converges conditionally; the absolute series behaves like \(1/\sqrt n\) and diverges.
C
nth-Term Test: the terms do not approach 0, so the series diverges.
D
Comparison with \(1/n
2
\) proves absolute convergence.
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