Ratio test, why does the (-1)^(n+1) disappear?

AI Thread Summary
In the ratio test, the term (-1)^(n+1) oscillates between -1 and 1, but it does not affect the limit as n approaches infinity. The test focuses on the absolute value of the ratio |An+1 / An|, which simplifies the calculations by allowing the oscillating terms to be disregarded. This is because the limit of the absolute values converges, while the oscillating signs do not impact the overall convergence behavior. Therefore, the oscillating factors can be factored out without affecting the outcome of the limit. The discussion clarifies that recognizing this allows for a simpler application of the ratio test.
CinderBlockFist
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In the book while doing the ratio test:

as n --> infinity

why do they just have (-1)^(n+1) just disappear in the next step, since it oscillates between -1 and 1, I don't understand how u could just make it disappear in computations. Isn't the limit as n -> infinity , equal to D.N.E.?
 
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I believe the ratio test tests the absolute value of |An+1 / An|. so the (-1)^n and (-1)^n+1 will just be one, so u can just take it out.
 
crap lol, i didn't even think of that. THanks cyrus, u da man!
 

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