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Does the series n factorial times 1 divided by e to the n converge or diverge?
Mantaray12
Use the ratio test: Let an = n!/en
lim n→∞ |an+1/an|
= lim n→∞ |[(n + 1)!/en+1]/(n!/en)
= lim n→∞ |[(n + 1)!/en+1](en/n!)
= lim n→∞ |[(n + 1)n!en]/(enn!e)
= (1/e) lim n→∞ (n + 1) = ∞, so the given series diverges.
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