maxpowers_00
Apr4-04, 09:13 PM
the question is can you come up with a power series whose interval of convergance is the interval (0,1] that is 0 < x < = 1 ? how about (0,infinity)? Give an explicit series of explain why you can't.
The first part of this question where they ask if a series can have an interval of (0,1). I dont think such a series can exist becaue when x=0 doesnt the series always converge, there for the series would have to be eqal to 0. so it can have an interval of [0,1) but not (0,1). but that would also mean a series can't have an interval of (0,infinity).
i just wan to know if it i am going the right way in my thinking and if, not if some one could point me in the right direction.
thanks
The first part of this question where they ask if a series can have an interval of (0,1). I dont think such a series can exist becaue when x=0 doesnt the series always converge, there for the series would have to be eqal to 0. so it can have an interval of [0,1) but not (0,1). but that would also mean a series can't have an interval of (0,infinity).
i just wan to know if it i am going the right way in my thinking and if, not if some one could point me in the right direction.
thanks