# Math Help - Can you do it?

1. ## Can you do it?

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

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?

3. So the first one is (-1)^n+1*x^n/(n) and the second is impossible since you couldn't tell where it would be centered?

4. yes on the first one

On the second If the radius of conv is inf the IC is (-inf,inf)

Since inf/2 = inf you can't have have IC (0,inf)