Proving Limit Exists with Cauchy Criterion for {X_n}

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Your N is not fixed; it should depend on \varepsilon only.

What's s?
Why did you pick p = 1?
 
mutton said:
Your N is not fixed; it should depend on \varepsilon only.

What's s?
Why did you pick p = 1?

give me a reason y i can't pick p=1

and bout the Sn
Sn= sum of the series from a1 to an

.
 
No one has to give you a reason why you can't pick p= 1. You are the one who is doing this. Please answer the question- why DID you pick p= 1?
 
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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