Can you cook up a power series whose interval of convergence is the interval (0,1]?How about (0, infinity)? Give an explicit series or explain

why you can't.

thanks

Results 1 to 4 of 4

- April 19th 2009, 04:28 PM #1

- Joined
- Jan 2009
- Posts
- 296

- April 19th 2009, 05:24 PM #2
for the first consder the power series representation of ln(x+1)

If your studies haven't got you this far look in the taylor series section.

For the second I'll give you a hint -- consider the radius of convergence

for a power series (0,inf) where would the power series be centered?

- April 19th 2009, 05:27 PM #3

- Joined
- Jan 2009
- Posts
- 296

- April 19th 2009, 05:30 PM #4