- #1
learningcalc
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Homework Statement
Determine whether the series converges or diverges
Sum from n=1 to infinity ((e^(1/n))/n)
Homework Equations
I am trying to use the limit comparison test to prove it.
The Attempt at a Solution
an = (e^(1/n))/n
bn = e/n
an/bn = e^(1/n)/e
lim n-> infinity an/bn = 1/e
Sum from n=1 to infinity e/n is divergent. (e/n = e(1/n). So sum from n=1 to infinity e/n = e*sum from n=1 to infinity 1/n. sum from n=1 to infinity 1/n is divergent because this is a p-series with n^p where p = 1. For p <= 1 the series is divergent.)
Since either both an and bn are convergent or both are divergent, an must be divergent as bn is divergent.
Thanks for any help.