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