Chapter 11 - Section 11.2 - Arithmetic and Geometric Sequences - Exercise Set - Page 647: 59

$\dfrac{11}{18}$

The expression $ \dfrac{1}{3(1)}+\dfrac{1}{3(2)}+\dfrac{1}{3(3)} $ evaluates to \begin{array}{l} \dfrac{1}{3}\left(\dfrac{1}{1}+\dfrac{1}{2}+\dfrac{1}{3} \right) \\\\= \dfrac{1}{3}\left(\dfrac{1(6)+1(3)+1(2)}{6} \right) \\\\= \dfrac{1}{3}\left(\dfrac{6+3+2}{6} \right) \\\\= \dfrac{1}{3}\left(\dfrac{11}{6} \right) \\\\= \dfrac{11}{18} .\end{array}