Thread: Converge or Diverge?

An = n^3 / (n + 5)

Can I just take the limit and say this is equal to 1 / 0 so it diverges?

Originally Posted by veronicak5678

An = n^3 / (n + 5)

Can I just take the limit and say this is equal to 1 / 0 so it diverges?

It diverges because this is equivalent to



Now what is the limit of that as it goes to infinity?

1 + 0 + 0 - 125/5 = -24 ?

What are you on about? You're subbing 1 here and 0 there. Take the limit as n goes to infinity

Originally Posted by Mathstud28

It diverges because this is equivalent to



Now what is the limit of that as it goes to infinity?

While that's true, isn't is much easier to simply take the original form of A_n and easily see that the limit is infinity as n approaches infinity?

I think that's more along the lines of what I was supposed to be doing, anyway...

So I'll just take the limit off the bat and say it diverges.

Originally Posted by veronicak5678

An = n^3 / (n + 5)

Can I just take the limit and say this is equal to 1 / 0 so it diverges?

and

Got it. Thanks!