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

I am maybe overthinking this, but what is the lim as n-> infinity of |(n+1)/(n+2)|

?

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 12:38pm
the 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 3:40pm
since (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.

## Answer this Question

## Related Questions

- CALC - please help me...for the power series summation of n^4x^n/2(n-1)factorial...
- calculus - interval of convergence - infinity of the summation n=0: ((n+2)/(10^n...
- calculus - interval of convergence - infinity of the summation n=0: ((n+2)/(10^...
- CALCULUS - find the radius and interval of convergence for the series the series...
- CALCULUS-URGENT - find the radius and interval of convergence for the series the...
- CALCULUS-URGENT- no one will respond!!! - find the radius and interval of ...
- Calculus 2 - In the following series x is a real number. In each case, use the ...
- calculus - ratio test - infinity of the summation n=1: (e^n)/(n!) [using the ...
- CALC 2 - a. Consider the following limit as a fact: lim n-> infinity ((n!)^1/...
- Calculus - How do I find the radius of convergence of a series where n=1 to ...

More Related Questions