Finding Intervals of Convergence

[abc617]

Find the interval of convergence for the given power series.
[PLAIN]http://img52.imageshack.us/img52/3632/c1786dba870d63ff1a827d9.png
The series is convergent
from x= ___ to
x = ____

Attempt


[PLAIN]http://img412.imageshack.us/img412/7411/image00.jpg


Attempted solutions:

I have to input the answer into something called WeBWorK and I've tried a bunch of different pairs of number, the only ones i remember try were

0, 8
0, 4
0, -8

among many others.

Can anyone tell me what I'm doing wrong?

 

[LCKurtz]

You have a sign mistake. You should get

$$\left| \frac{x-4} 4\right| < 1$$

so

$$-1 < \frac{x-4} 4 < 1$$

 

[abc617]

Well after simplifying that inequality, I get the intervals to be (x=0, x=8), and like I said before, it still isn't correct.

Did I make a mistake somewhere else?

 

[LCKurtz]

No. It converges on (0,8). The only remaining question is whether it converges at the two end points, 0 and 8, which need to be checked separately. You might need to give an answer in one of these forms:

(0,8), [0,8), (0,8], [0,8]

where the square bracket indicates convergence at that end. Check x = 0 and x = 8.