Answer:
[tex]e^{\frac{1}{5}x} = \sum\limits^{\infty}_{k=0} \frac{1}{5}^k \cdot \frac{x^k}{k!}[/tex]
Step-by-step explanation:
Poorly formatted question.
The given parameters can be summarized as:
[tex]e^x = \sum\limits^{\infty}_{k=0} \frac{x^k}{k!}[/tex] ----- the series
Required
Determine [tex]e^\frac{1}{5}^x[/tex]
We have:
[tex]e^x = \sum\limits^{\infty}_{k=0} \frac{x^k}{k!}[/tex]
Substitute [tex]\frac{1}{5}x[/tex] for x
[tex]e^{\frac{1}{5}x} = \sum\limits^{\infty}_{k=0} \frac{(\frac{1}{5}x)^k}{k!}[/tex]
Split
[tex]e^{\frac{1}{5}x} = \sum\limits^{\infty}_{k=0} \frac{1}{5}^k \cdot \frac{x^k}{k!}[/tex]
