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

In summary, the (-1)^(n+1) term is included in the ratio test for mathematical convenience, but it does not affect the convergence or divergence of the series. It can be ignored when using the test, as it does not impact the result. The term is always present in the formula, but it does not play a direct role in the test. It is included to ensure that the test can be applied to a variety of series without needing to modify the formula.
  • #1
CinderBlockFist
86
0
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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  • #2
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.
 
  • #3
crap lol, i didn't even think of that. THanks cyrus, u da man!
 

1. Why does the (-1)^(n+1) term disappear in the ratio test?

The (-1)^(n+1) term disappears in the ratio test because it is a constant term that does not affect the convergence or divergence of the series. It is simply included in the ratio test for mathematical convenience, but it does not have any significant impact on the result.

2. Can I ignore the (-1)^(n+1) term when using the ratio test?

Yes, you can ignore the (-1)^(n+1) term when using the ratio test. As mentioned before, it does not affect the convergence or divergence of the series, so it can be omitted without changing the result of the test.

3. How does (-1)^(n+1) affect the ratio test?

The (-1)^(n+1) term does not directly affect the ratio test. It is included in the test as part of the general formula, but it does not play a role in determining the convergence or divergence of the series.

4. Is the (-1)^(n+1) term always present in the ratio test?

Yes, the (-1)^(n+1) term is always present in the ratio test formula, but it can be ignored when performing the test as it does not have any impact on the result.

5. Why is the (-1)^(n+1) term included in the ratio test if it doesn't affect the result?

The (-1)^(n+1) term is included in the ratio test for mathematical convenience. It is a standard part of the formula and is used to ensure that the test can be applied to a wide range of series without needing to modify the formula each time.

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