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Math Help - Quick question about Taylor Polymonials

  1. #1
    Senior Member Educated's Avatar
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    Quick question about Taylor Polymonials

    Quick question:

    When they ask for the 'fifth' term of a particular taylor polymonial, which term are they asking for?

    Eg. If I had the McLauren series for e^x = 1 + \dfrac{x}{1!} + \dfrac{x^2}{2!} + \dfrac{x^3}{3!} + \dfrac{x^4}{4!} + \dfrac{x^5}{5!} + \dfrac{x^6}{6!} + ...

    Do they mean the fifth one \dfrac{x^4}{4!} or do they mean the x^5 term?
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  2. #2
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    Re: Quick question about Taylor Polymonials

    Since the polynomial starts with x^0, the fifth term is x^4.
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  3. #3
    Senior Member Educated's Avatar
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    Re: Quick question about Taylor Polymonials

    What if the Taylor polynomial has zero coefficient terms in it? Eg.

    1 - \dfrac{x^2}{2!} + \dfrac{x^4}{4!} - \dfrac{x^6}{6!} + ...

    Would the third term be \dfrac{x^4}{4!}
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