Show Cauchy Sequence iff Subsequence is Quasi-Cauchy

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Quasi-Cauchy help!

Show that a sequence is Cauchy iff every subsequence is quasi-Cauchy?


A sequence (xn) is called a quasi-Cauchy sequence if for all epsilon greater than 0 there exists N such that |xn+1 − xn| < epsilon.


Help please...
 
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Hi, we'll be happy to help you iron out problems with your proof, or provide hints in the right direction...but first you have to show us what you've done already.
 

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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