Answer
$1+\sum_{k=1}^{\infty} \dfrac{x^k}{2k}$
Work Step by Step
We are given the power series $1+\dfrac{x}{2}+\dfrac{x^2}{4}+\dfrac{x^3}{6}+...$
The given series can be represented in the summation form as:
$1+\dfrac{x}{2}+\dfrac{x^2}{4}+\dfrac{x^3}{6}+...=1+\sum_{k=1}^{\infty} \dfrac{x^k}{2k}$
