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How to get to this limit?

1. Homework Statement
Find the limes of the equation, so lim n ->

2. Homework Equations
m1.png


3. The Attempt at a Solution
I tried to solve this by using the third binomial formula and formed this to
m2.png

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

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1. Homework Statement
Find the limes of the equation, so lim n ->

2. Homework Equations
m1.png


3. The Attempt at a Solution
I tried to solve this by using the third binomial formula and formed this to
m2.png

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.
 
Last edited:
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

Science Advisor
Homework Helper
Insights Author
Gold Member
2018 Award
9,510
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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}##?
 

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