(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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.)

2. Relevant equations

n/a

3. 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?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Determining convergence of infinite series with factorial without ratio test

**Physics Forums | Science Articles, Homework Help, Discussion**