# Once i find the radius of convergence, how do i find the interval of convergence?

1. Mar 9, 2006

### mr_coffee

Hello everyone, i'm confused (as usual). I think i found the radius of convergence but then waht do i do to find the interval on which it converges?

The directions says:
Find all the values of x such that the given series would converge.
http://cwcsrv11.cwc.psu.edu/webwork2_files/tmp/equations/70/aaf16ffcdb10d6976585856b5dafca1.png [Broken]
The series is convergent
from x = , left end included (enter Y or N):
to x = , right end included (enter Y or N):

Here is my work:
http://img90.imageshack.us/img90/6637/lastscan5ox.jpg [Broken]

Any help would be great! thankss!

Last edited by a moderator: May 2, 2017
2. Mar 9, 2006

### mr_coffee

OKay i had to of messed up finding the radius of convergence. I looked at a tutoiral and it should be right...
I got
(-7,7); for the interval, which was wrong though. Can you see where i screwed it up? it should be open brackets i got that part right

Okay i did it again, and i tried (-14,14), now i have 75% of the question rgiht, so either -14 is wrong or 14 is wrong but i don't see how u can get any other number then that.
if u have
|(x-7)/7| < 1

and
|(x-7)/7| > 1

Last edited: Mar 9, 2006
3. Mar 9, 2006

### HallsofIvy

Staff Emeritus
Why did $\left|\frac{x-7}{7}\right|< 1$ become x-7< 7??
Shouldn't it be |x-7|< 7? And doesn't that mean that -7< x- 7< 7?
So that 0< x- 7< 14?

4. Mar 9, 2006

### mr_coffee

Thanks Ivey ur the man! i forgot all about that rule!
w00t.