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Calculus

Approximate the sum of the series correct to four decimal places.
n=1 to infinity
(-1)^n/4^n*n!

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Sarah

  1. If you notice that the Taylor's series expansion of
    e^(-x/4) =
    1-x/4+x^2/32-x^3/384+x^4/6144-...
    is exactly the given series less the first term with x=1,
    so
    the given series is
    e^(-1/4)-1 = -0.2212 to four places.

    If you sum term by term, you just need to sum until the next term falls below 0.00001, which is around the 5th term.

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    MathMate

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