# Thread: Maclaurin Series and Term by Term Integration

1. ## Maclaurin Series and Term by Term Integration

Hey

"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.

I. -2<x<2
II. -2<= x < 2
III. -2 < x <= 2
IV. -2 <= x <= 2

It can be more than one.