$\dfrac{1}{1 \times 2} + \dfrac{2}{2 \times 4} + \dfrac{3}{4 \times 7} + \dfrac{4}{7 \times 11} + \dfrac{5}{11 \times 16}$
$= 1 - \dfrac{1}{2} + \dfrac{1}{2} - \dfrac{1}{4} + \dfrac{1}{4} - \dfrac{1}{7} + \dfrac{1}{7} - \dfrac{1}{11} + \dfrac{1}{11} - \dfrac{1}{16}$
$= 1 - \dfrac{1}{16}$
$= \dfrac{15}{16}$