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

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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}##?
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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