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January 29, 2015

January 29, 2015

Posted by **Luma** on Saturday, October 20, 2012 at 10:50am.

?

I am trying to use the ratio test to find interval of convergence for the infiinite series (n/n+1)((-2x)^(n-1))

so i did the limit of |(n+1)/(n+2)| but i am wondering if the limit is simply =1, or if it is infinity/infinity so use l'hopital's rule???

maybe i am overthinking it and the limit is just 1.

thank you for your assistance

- Calculus -
**Reiny**, Saturday, October 20, 2012 at 12:38pmthe limit of your problem is 1

as n --> infinity , both numerators and denominator are practiacally the same, with the denominator being one less than the numerator.

e.g. if n = 1 000 000

then we have 1 000 001/1 000 002 , pretty close to 1 wouldn't you say?

- Calculus -
**Steve**, Saturday, October 20, 2012 at 3:40pmsince (n+1)/(n+2) = 1 - 1/(n+2) it is clear that as n grows, the value approaches 1.

Yes, L'Hopital's Rule also works, since you have infinity/infinity. taking derivatives gives 1/1 as the limit.

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