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Math Help - Taylor's theorem and e

  1. #1
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    Taylor's theorem and e

    Explain why Taylor's Theorem guarantees that we can use a Taylor polynomial to estimate the value of e to any degree fesired
    the taylor series for e is
    1/0! + 1/1! * x + 1/2! * x^2 + 1/3! * x^3 + ... 1/n! * x^n

    I really have no clue on this one. We never talked about e in class.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by diroga View Post
    the taylor series for e is
    1/0! + 1/1! * x + 1/2! * x^2 + 1/3! * x^3 + ... +1/n! * x^n

    I really have no clue on this one. We never talked about e in class.
    You don't need to have, all you need is that you have done Taylor's theorem and know at least one form of the remainder for a truncated Taylor series and the general term of the series in question.

    Now what you have to do is show that for fixed x the remainder can be made as small as you like by truncating sufficiently far to the right in the series.

    CB
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