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there is a proof of the ratio test that I have seen a couple of times here:

http://tutorial.math.lamar.edu/Classes/CalcII/RatioTest.aspx

I dont know how to use latex, so abs(x) will mean absolute value

I am ok with this:

abs( a_{N+1}) < r abs(a_{N})

I dont understand where the r^{2}come from in the next line

abs( a_{N+2}) < r abs(a_{N+1})< r^{2}abs(a_{N})

Similarly, I dont understand how to get to the generalization of

abs( a_{N+k}) < r^{k}abs(a_{N+1})

I should probably add that I understand all other aspects (i.e. using comparison test), but since I don't understand this part, my understanding of the proof fails.

Thanks,

Ivan77

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# Question about one part of the Ratio Test proof

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