identify the function represented by the following power series. ∑(k = 1 to ∞) x^k/k click the icon to view…

identify the function represented by the following power series. ∑(k = 1 to ∞) x^k/k click the icon to view a table of taylor series for common functions. f(x)=□

identify the function represented by the following power series. ∑(k = 1 to ∞) x^k/k click the icon to view a table of taylor series for common functions. f(x)=□

Answer

Explanation:

Step1: Recall Taylor - series formula

The Taylor - series expansion of $\ln(1 - t)=-\sum_{k = 1}^{\infty}\frac{t^{k}}{k}$, for $|t|\lt1$.

Step2: Identify the function

Let $t=-x$. Then $\sum_{k = 1}^{\infty}\frac{x^{k}}{k}=-\ln(1 - x)$ for $|x|\lt1$.

Answer:

$-\ln(1 - x)$