Limit question: lim as n->infinity of: 2n^4/(n + 1)^4

[MarkSA]

Hello,

I have a limit I need to evaluate in a series problem. It is:

Limit as n->infinity of: 2n^4/[(n + 1)^4]

I really don't want to multiply (n+1)^4 out and then multiply top and bottom by 1/n^4 to evaluate it. Are there easier ways/tricks to do this one?

 

[PAULK]

Hello,

I have a limit I need to evaluate in a series problem. It is:

Limit as n->infinity of: 2n^4/[(n + 1)^4]

I really don't want to multiply (n+1)^4 out and then multiply top and bottom by 1/n^4 to evaluate it. Are there easier ways/tricks to do this one?

Yes.

I suppose you actually want to see one, right?

2n^4
------------- =
(n+1)^4

2
-------------
(n+1)^4 /n^4

2
---------------
(1+1/n)^4

Now you want lim n -> infinity?

 

[MarkSA]

Thanks. It's 2.

 

[Dr. Flim-Flam]

Repeated use of L'Hopital will do it.