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

Answer 1

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

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