- #1
emr13
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Homework Statement
Determine whether the series below is convergent or not:
[tex]\sum 7*\frac{n!}{n^{n-10}}[/tex]
n=8 and the series goes to infinity
(Sorry, I couldn't get the formatting correct.)
Homework Equations
n/a
The Attempt at a Solution
Well, originally I thought the series was divergent, and used the nth Term Test to prove it. Except that gave me infinity over infinity. I stopped there because I can't use L'Hospital's rule because I don't know how to derive factorials.
We use a computer program to enter answers, and it told me the series didn't diverge. So I know it converges. However, I have no idea how to prove that, and an explanation is required with my answer.
I know that the Ratio test is used for series with factorials, but we have not been taught that yet. The Alternating Series doesn't apply, and I don't think the p-series test applies directly.
So that leaves the Comparison and the Limit Comparison tests. What series should I use to compare? And is there any way to get rid of the factorial?