Converge or diverge? (partial frac. long division)

[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 I am stuck on the long division, haven't done it in so long can't remember how to. any tips would be great.

 

[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?

 

[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?

 

[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.

 

[SciSteve]

are you sure you don't 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]

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.