(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find the interval of convergence of the infinite series:

∞

∑ (x-1)^{n}/ 2^{n}

n = 1

2. Relevant equations

Using the ration test. It converges if the absolute value of the limit of f(n+1)/f(n) as n -> ∞ < 1.

Well, I hope that's how you write it. I'm sure you guys know how to use the ration test.

3. The attempt at a solution

I actually believe I have the answer. But I have no way of knowing if it is right.

Here is my answer:

The interval of convergence is -1 < x < 3.

I got this by using the ratio test, and then eliminating factors of (x-1)^{n}and 2^{n}(after expanding the exponents), leaving me with the limit of

lim (x-1)/2 as n -> ∞

Then, since there is no n, then that limit IS (x -1)/2 (unless I'm totally off)

And the absolute value of that has to be less than 1 for it to converge, so

-1 < (x-1)/2 < 1

-2 < x - 1 < 2

-1 < x < 3

Is this correct? Do you need me to post the part where I canceled out terms before I took the limit?

Thanks!

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Finding an Interval of Convergence

**Physics Forums | Science Articles, Homework Help, Discussion**