# Converge or diverge? (partial frac. long division)

Determine whether the sequence converges or diverges. If it converges, find the limit.
An=7+4n^2/n+2n^2
I know you have to compare it to the integral of the same equation, so I do this and the only means of integration I believe to be is by partial fractions, since degree of top equals degree of bottom but im stuck on the long division, haven't done it in so long can't remember how to. any tips would be great.

## Answers and Replies

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Dick
Homework Helper
Forget the integral test for sequences. That's for summing series. To find the limit think about dividing the numerator and denominator by n^2. Does that ring a bell?

the only thing is it says if it converges find the limit and i know it doesn't diverge so I need to find out the value do i still take the integral of it or what?

all you ever do with sequences to find the value they approach is take the limit of it as n -> inf of your general term.

when you find the limit of a sequence all you do is take the limit of it. That's it.

are you sure you dont take the integral or derivative? because if not there must be a trick to this one i find that the lim as n->inf. goes to 0 when plugging into the original given equation, but that isn't the right answer, any ideas?

Dick