Use an appropriate series in (2) in Section 6.1 to find the Maclaurin series of the given function. Write your answer in summation notation.

Question

Use an appropriate series in (2) in Section 6.1 to find the Maclaurin series of the given function. Write your answer in summation notation. 1 5 x

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Khang Minh 3 years 2021-08-11T20:04:18+00:00 1 Answers 8 views 0

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  1. huyenthanh
    0
    2021-08-11T20:05:27+00:00
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    Answer:

    e^{\frac{1}{5}x} = \sum\limits^{\infty}_{k=0} \frac{1}{5}^k \cdot \frac{x^k}{k!}

    Step-by-step explanation:

    Poorly formatted question.

    The given parameters can be summarized as:

    e^x = \sum\limits^{\infty}_{k=0} \frac{x^k}{k!} —– the series

    Required

    Determine e^\frac{1}{5}^x

    We have:

    e^x = \sum\limits^{\infty}_{k=0} \frac{x^k}{k!}

    Substitute \frac{1}{5}x for x

    e^{\frac{1}{5}x} = \sum\limits^{\infty}_{k=0} \frac{(\frac{1}{5}x)^k}{k!}

    Split

    e^{\frac{1}{5}x} = \sum\limits^{\infty}_{k=0} \frac{1}{5}^k \cdot \frac{x^k}{k!}

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