Hello,

I'm having difficulty determining the behavior of this series.

"Show that the series: $\displaystyle \sum_{n=1}^{\infty} \frac{5n+1}{8n^2-10n-52}$ converges or diverges by finding a p-series, $\displaystyle \sum_{n=1}^{\infty}\frac{c}{n^p}$ or geometric series, $\displaystyle \sum_{n=1}^{\infty}cr^n$ to use in the comparison test.

Your answer should consist of four items separated by commas.

- The first item should be either the word
**less** or the word **greater**. - The second item should be an expression for the term bn of the series used in the comparison test.
- The third item should be a natural number N so that the comparison inequality an < bn holds for all n > N or an > bn holds for all n > N
- The fourth item should be the word
**converges** or the word **diverges** to indicate whether you are saying that the given series Sum(an,n=1..infinity, i.e., , converges or diverges."

I compared $\displaystyle \frac{5n+1}{8n^2-10n-52}$ with $\displaystyle \frac{5}{8n}$

saying that

$\displaystyle \frac{5n+1}{8n^2-10n-52}$ > $\displaystyle \frac{5}{8n}$ for n > 4.

And since $\displaystyle \frac{5}{8n}$ is divergent by p-series, that

$\displaystyle \frac{5n+1}{8n^2-10n-52}$ was also divergent.

So my answer looks like:

greater,(5/8)(1/n),4,diverges

which is incorrect. If anyone can point out where I've gone wrong, I would greatly appreciate it.