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Math Help - Maclaurin Series and Term by Term Integration

  1. #1
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    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.

    Thanks for your help
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  2. #2
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    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.
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