## Thomas' Calculus 13th Edition

$\dfrac{x}{x-1}$
Here, $a=1$ and common ratio $r =\dfrac{1}{x}$ Formula to calculate the sum of a geometric series is: $S=\dfrac{a}{1-r}$; Thus, $S=\dfrac{1}{1-\dfrac{1}{x}}$ or, $S=\dfrac{x}{x-1}$