Proving Cauchy Sequence with Triangle Inequality

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Homework Statement



Let Sn be a sequence such that |Sn+1-Sn|< 2-n for all n in the natural numbers

Homework Equations





The Attempt at a Solution



I understand what it means to be cauchy but I'm not sure how to prove this particular sequence is cauchy. Please help!
 
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Use the triangle inequality. For m>n, |S_m-S_n|<=|S_m-S_(m-1)|+|S_(m-1)-S_(m-2)|+...+|S_(n+1)-S_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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