- #1
tangibleLime
- 71
- 0
Homework Statement
Test the series for convergence or divergence.
Homework Equations
The Attempt at a Solution
I started playing around with it, trying to write it in different ways, and got it down to something that *looked* like a p-series... but there's an 'n' in the exponent. Does this still make the p-series test valid?
[tex]\sum_{n=1}^{\infty} \frac{(7n+1)^{n}}{n^{9n}}[/tex]
I removed the one because it seems like it would make no difference as n -> infinity.
[tex]\sum_{n=1}^{\infty} \frac{(7n)^{n}}{n^{9n}}[/tex]
[tex]\sum_{n=1}^{\infty} \frac{7}{n^{8n}}[/tex]
Factoring out the 7...
[tex]7 * \sum_{1}^{\infty} \frac{1}{n^{8n}}[/tex]
I figure since n is always positive and greater than 0, the power 8n will follow the same standards. And 1/n^p is a p-series, and the p in this case is 8n. But is this still valid since there's an 'n' in the power?