Is the series #\sum_(n=1)^\infty n e^(-n)# absolutely convergent, conditionally convergent or divergent?

(Use the appropriate test)

(Use the appropriate test)

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Apr 20, 2018

Answer:

Converges

Explanation:

Apply the ratio test:

# lim_(n to oo ) |a_(n+1)/a_n | #

# = lim_(n to oo ) |((n+1) e^(-(n+1)))/(n e^(-n)) | #

# = lim_(n to oo ) |((1+1/n) )/( e) | = 1/e lt 1#

It converges :)

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