## University Calculus: Early Transcendentals (3rd Edition)

$\dfrac{116,402}{37,037}$ or, $\dfrac{22}{7}$
We have: $3.\overline{142857}=3+\Sigma_{n=0}^\infty \dfrac{142857}{10^6}\dfrac{1}{(10^6)^n}$ The sum of a geometric series can be found as: $S=\dfrac{a}{1-r}$ Thus, $S=3+\dfrac{\dfrac{142857}{10^6}\dfrac{1}{(10^6)^n}}{1-10^6}=\dfrac{116,402}{37,037}$ or, $\dfrac{22}{7}$