Maclaurin Series and Term by Term Integration
"Suppose the interval of convergence of the Maclaurin series for f(x) is -2<x<2. If the Maclaurin series for the integral of f(t) dt from 0 to x is obtained by integrating term by term, which of the following could be the interval of convergence of the new series? Justify.
II. -2<= x < 2
III. -2 < x <= 2
IV. -2 <= x <= 2
It can be more than one.
Thanks for your help
Re: Maclaurin Series and Term by Term Integration
I would say all, because it depends on your the series you are interested in. If you give a particular series there are tests that can be used to determine which possibility it would be. (It's only all of them because of the word "could" within the question.)
P.S. I might be wrong. =P
P.P.S. But I think I'm right.