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

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- Apr 19th 2009, 03:28 PM #1

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- Apr 19th 2009, 04:24 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?

- Apr 19th 2009, 04:27 PM #3

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- Apr 19th 2009, 04:30 PM #4