Okay whats going on here....

I have no idea how to solve sequence problems. What is the trick? I'm

talking about convergent/divergent problems. My book does a bad job

at explaining them-it has all this jarjon like "well if X>a and n>epsilon then

for all numbers when plotted to infinity" yadda (lol I know I posted jarjon

on purpose) sorry if I sound like a jerk, I'm just frusturated at the moment.(Headbang)

Here's where it didn't make sense:

an=2^n/(3^n+1)

and (2n-1)!/2n+1! The author did some weird manipulation to get the solutions (trying to find out divergence or convergence) and I have no idea

what or even why he did what he did lol. Any help would be greatly appreciated!