How to Approach Finding the Limit of an Equation as n Approaches Infinity?

[ingo23]

Homework Statement

Find the limes of the equation, so lim n -> ∞

Homework Equations

[/B]

The Attempt at a Solution

I tried to solve this by using the third binomial formula and formed this to

I wanted to show that it's <= 1/n, but then I checked wolfram alpha and it seems like it actually conv. against sqrt(2), but how do I get there?

 

[PeroK]

Homework Statement

Find the limes of the equation, so lim n -> ∞

Homework Equations

[/B]

The Attempt at a Solution

I tried to solve this by using the third binomial formula and formed this to

I wanted to show that it's <= 1/n, but then I checked wolfram alpha and it seems like it actually conv. against sqrt(2), but how do I get there?

Actually, you are nearly there. Just one or two small steps.

 

[ingo23]

Actually, you are nearly there. Just one or two small steps.

Thats good to know, but can you give me a pointer towars the right direction?
All I managed to do is pull the sqrt(4) out of the numerator, but I this doesn't relly help me since I can't see a way to get rid of the square roots in the denominator. :/

 

[PeroK]

Thats good to know, but can you give me a pointer towars the right direction?
All I managed to do is pull the sqrt(4) out of the numerator, but I this doesn't relly help me since I can't see a way to get rid of the square roots in the denominator. :/

Why not divide top and bottom by $\sqrt{n}$?