Question

$\sum _{n=0}^{\infty }\frac{(\ln x{)}^n}{n!}$ is equal to

• A. $\ln x$
• B. $x$
• C. $\frac{1}{\ln x}$
• D. $\frac{1}{x}$

Answer 1

The correct option is B $x$

Expanding the above series, we get the sum $=1+\frac{\ln \left(x\right)}{1!}+\frac{\left(\ln \right(x){)}^2}{2!}+...\infty$
$=e^{\ln \left(x\right)}$$=x$