Question 1009855
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It is not converged.


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<U>Comment from student</U>: Hi you say (- 1)^r - 1 is divergent yet (- 1)^r - 1 x b can be proved convergent if b > 0 
This can be easily seen if b = 1/n...now if b = 1 the above doesn't change yet you claim it is still convergent..can you explain why? 
Best wishes,thx,Colin
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<U>My response</U>. 

<pre>
1) Yes, the series { {{{(-1)^(r-1)*b^r}}} } with the constant b, |b| < 1, is converged. It is geormetric progression,  by the way.

2) Yes, the series {{{(-1)^(r-1)}}} is not converged. It is diverged.

These two series are different. They are not the same. Do not miss them. 
Different series have different properties. 

3) Read these two links

https://en.wikipedia.org/wiki/Convergent_series

and

http://tutorial.math.lamar.edu/Classes/CalcII/ConvergenceOfSeries.aspx
(example 3).
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