Convergent series and their corresponding sequences (analysis course)

v.rad
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If a_n >= 0 for all n, and the series a_n converges, then n(a_n - a_n-1) --> 0 as n --> infinity.

Prove or disprove the statement using a counterexample.

I know that the statement is false...I am just having terrible difficultly finding a counterexample...
 
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actually... http://www.mathhelpforum.com/math-help/f57/limit-question-indeterminate-forms-159597.html
 

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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