Calc II Power Series
sum (1,∞) of (x-3)^n/(n*2^n)
I'm supposed to use the ratio test to find the radius of convergence.

so I did lim n-∞ of (x-3)^(n+1)/(n+1)*2^(n+1) * n*2^n/(x-3)^n

so isn't it lim n-∞ of (x-3)/2?

If it isn't, how do I figure out this problem? (I know the answer is 2)

Question

Calc II Power Series
sum (1,∞) of (x-3)^n/(n*2^n)
I'm supposed to use the ratio test to find the radius of convergence.

so I did lim n->∞ of (x-3)^(n+1)/(n+1)*2^(n+1) * n*2^n/(x-3)^n

so isn't it lim n->∞ of (x-3)/2?

If it isn't, how do I figure out this problem? (I know the answer is 2)

zarkon · Answer

$$\frac{|x-3|}{2}<1$$

$$|x-3|<2$$

anonymous · Answer

that's what I thought too..
but wouldn't (x-3)<2 simplify to x<-1?

zarkon · Answer

it's not (x-3)<2 

it is 

|x-3|<2

anonymous · Answer

sorry, don't know how to make absolute value bars. is it illegal in math to add the 3 over then? (that's really embarrassing that I can't remember that)

zarkon · Answer

when you have |x-3|<2 that gives you x-3<2 and -(x-3)<2 x-3<2 => x<5 and -(x-3)<2=>x-3>-2 => x>1 so 1

anonymous · Answer

okay awesome, thanks for your help. hopefully I can do all the other problems like this now. :D