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

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Homework Help Overview

The discussion revolves around finding the limit of an equation as n approaches infinity, specifically focusing on the convergence behavior of the expression involved.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss using the third binomial formula and consider bounding the expression by 1/n. There is mention of checking results against computational tools like Wolfram Alpha, which suggests convergence to sqrt(2). Questions arise about how to simplify the expression, particularly regarding the presence of square roots in the denominator.

Discussion Status

Some participants indicate they are close to a solution and seek further guidance on specific steps. Suggestions have been made to manipulate the expression by dividing terms, indicating a collaborative effort to explore different approaches.

Contextual Notes

There is a focus on the manipulation of limits and the handling of square roots, with participants expressing uncertainty about the best methods to simplify their expressions. The discussion reflects a learning process without clear consensus on the next steps.

ingo23
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Homework Statement


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

Homework Equations


m1.png
[/B]

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?
 
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ingo23 said:

Homework Statement


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

Homework Equations


m1.png
[/B]

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:
PeroK said:
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. :/
 
ingo23 said:
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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