Originally posted by eldragonfly
can somebody walk me through it please. Also forgot how to take the limit of a series also.
when talking about finding the limit of a series (i'll assume it's in closed form, with n incrementing from some constant to infinity), you will be trying to figure out if the series diverges to infinity or converges to some constant.
A prerequisite for convergence is that the general term of the series - the general expression in closed form that is being incremented - must have a limit of 0 as n approaches infinity. This is a necessary condition for convergence, but insufficient proof that the series will converge.
Additional tests for seeking proof or disproof of convergence of a series, include but are not limited to: the "power test," the ratio test, the comparison test, the limit comparison test, the improper integral test. Fundamentally, most of these methods basically involve comparing your specific series to more general series whose convergence or divergence is already known. They are attempts at answering the question "does my series act more like a geometric series (convergence), or like a harmonic/arithmetic series (divergence)?" This is my personal take on the idea behind the tests; don't take it as gospel.
if you need specifics on these tests, i could try to elaborate, but i'm sure you'll find more readable resources (.pdf documents, or wikipedia entries) that would be more useful than awkward forum notation