Chapter 11 - Infinite Sequences and Series - 11.2 Exercises - Page 736: 53

$2.516516 =\frac{838}{333}$

$2.516516516516516$ $=2+\frac{516}{10^{3}}+\frac{516}{10^{6}}+...$ $=2 \Sigma^{\infty}_{n=1} 516(\frac{1}{10^{3}})^{n}$ $a=\frac{516}{10^{3}}$ and $r=\frac{1}{10^{3}}$ $2.516516516516516=2+\frac{\frac{516}{10^{3}}}{1-\frac{1}{10^{3}}}$ $=2+\frac{516}{999}$ $=\frac{2514}{999}$ $=\frac{838}{333}$