Check Convergence of sum_(n+1)^infty (-1)^n * (e^n/n!)

Jaslyn Sloan 2022-11-19 Answered
Check Convergence of n + 1 ( 1 ) n ( e n n ! )
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Answers (1)

mainzollbtt
Answered 2022-11-20 Author has 13 answers
Let us put
a n := e n n ! a n + 1 a n = e n + 1 ( n + 1 ) ! n ! e n = e n + 1 n 0
Thus, the series converges absolutely and thus it also converges, i.e.:
n = 1 e n n ! converges n = 1 ( 1 ) n e n n ! also converges
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