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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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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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