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

1. Apr 15, 2008

### SciSteve

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.

2. Apr 15, 2008

### Dick

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?

3. Apr 15, 2008

### SciSteve

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?

4. Apr 15, 2008

### rostbrot

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.

5. Apr 15, 2008

### SciSteve

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?

6. Apr 15, 2008

### Dick

I am REALLY sure that i) there is no use in taking the integral and ii) you don't need to take the derivative. The limit as n->inf does not go to 0. I already told you what to do. Divide the numerator and denominator by n^2 and then take a another look at it.