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Math Help - Question on Alternating Series

  1. #1
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    Question on Alternating Series

    I have a question on interpreting sigma notation. Is this accurate?

    e^{-x^2} = \sum_{n=0}^\infty \frac{(-x^2)^n}{n!} = \sum_{n=0}^\infty \frac{x^{2n}}{n!}

    It seem like it must be, but I'm not sure, so I wanted to confirm. It seems to me that if you have a negative variable raised to an even power, it must always be positive. But then, this series is no longer alternating, which seems wrong.

    Any advice is appreciated.

    Thanks.
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  2. #2
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    Re: Question on Alternating Series

    Quote Originally Posted by joatmon View Post
    I have a question on interpreting sigma notation. Is this accurate?
    e^{-x^2} = \sum_{n=0}^\infty \frac{(-x^2)^n}{n!} = \sum_{n=0}^\infty \frac{x^{2n}}{n!}
    It should be e^{-x^2} = \sum_{n=0}^\infty \frac{(-x^2)^n}{n!} = \sum_{n=0}^\infty \frac{(-1)^nx^{2n}}{n!}
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