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

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.

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:



Any help would be great! thankss!

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

HallsofIvy

Why did [itex]\left|\frac{x-7}{7}\right|< 1[/itex] 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?

mr_coffee

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