Radius of convergence of an infinite series.
(Interval of convergence)
http://tinypic.com/r/dyty4k/6

Question

Radius of convergence of an infinite series.
(Interval of convergence)
http://tinypic.com/r/dyty4k/6

hartnn · Answer

from the ratio test as explained below, i got R =4, did you get that too ?

hartnn · Answer

then interval would be (1-4,1+4) = (-3,5)

anonymous · Answer

I think I tried that. but maybe I used [-3,5] instead. Thank you

anonymous · Answer

That was wrong :( shold we test the end points?

hartnn · Answer

yes, didn't (-3,5) work ?? 
endpoints makes the series divergent, so its not [-3,5]

anonymous · Answer

no because that means inclusive

hartnn · Answer

actually, (-3,5) means -3 and 5 are NOT included.

hartnn · Answer

also, we need to exclude 4, right ?

anonymous · Answer

yes

hartnn · Answer

so, maybe try  (-3,4)U (4,5)

anonymous · Answer

@byerskm2 in the picture, it seem you have(3,5) ? a "+3"?

anonymous · Answer

I used a -, sorry

anonymous · Answer

(-3,4)U (4,5) is also wrong :P

anonymous · Answer

$$|x-1|^2<4\implies x-1<2,\quad x-1>-2\ x<3, x>-1 (-1,3)$$

anonymous · Answer

try (-1,3)

anonymous · Answer

!!! YES! Okay can we go overhow you got that?

anonymous · Answer

ohhh, okay, that makes sense :) thanks guys!

anonymous · Answer

well, I said, a geometrical series can converge iff the terms keep decreasin

anonymous · Answer

using given method, $$C_n=\frac{(x-1)^2}{4^n}$$solving gives R=2
I think you went wrong in taking "R=4"