Sequences - Assumption that I need to confirm about n approaching infinity

[unixmd5crypt]

Homework Statement

Find the limit:
a_n= 2n/(n²+1)^1/2

Homework Equations

n/a

The Attempt at a Solution

Because n is approaching infinity, is it OK to disregard the +1 in the denominator and just consider the denominator to be n? This would then divide out the n in the numerator leaving 2 which is the correct answer. I think this is acceptable, but I wanted to run it by you all to confirm. Thank you in advance for your help.

 

[rock.freak667]

Yes you can consider the limit like that, the '1' becomes negligible as n gets bigger and bigger.

 

[unixmd5crypt]

great, that was what I thought but I wanted to make sure that what I got and the correct answer weren't just a great coincidence. Thanks for the fast reply! :)

 

[physicsman2]

factor out an n^2 in the denominator in the square root to get: sqrt((n^2)(1+(1/n^2))).

then the problem should be something like: (2n)/[(n)(sqrt(1 + (1/n^2)))].

Apply the properties of a limit taken to infinity and you should get 2 as your limit.

So in essence, you could ignore the 2, but to show why you can ignore it, you can do what I just showed you.