$\frac{1}{1.6}$ + $\frac{1}{6.11}$ + $\frac{1}{11.16}$ + $\frac{1}{16.21}$ +...+ $\frac{1}{2006.2011}$ + $\frac{1}{2011.2016}$
= $\frac{1}{5}$ . ($\frac{5}{1.6}$ + $\frac{5}{6.11}$ + $\frac{5}{11.16}$ + $\frac{5}{16.21}$ +...+ $\frac{5}{2006.2011}$ + $\frac{5}{2011.2016}$)
= $\frac{1}{5}$ . ($\frac{1}{1}$ - $\frac{1}{6}$ + $\frac{1}{6}$ - $\frac{1}{11}$ + $\frac{1}{11}$ - $\frac{1}{16}$ + $\frac{1}{16}$ - $\frac{1}{21}$ +...+ $\frac{1}{2006}$ - $\frac{1}{2011}$ + $\frac{1}{2011}$ - $\frac{1}{2016}$)
= $\frac{1}{5}$ . ($1$ - $\frac{1}{2016}$)
= $\frac{1}{5}$ . ($\frac{2016}{2016}$ - $\frac{1}{2016}$)
= $\frac{1}{5}$ . $\frac{2015}{2016}$= $\frac{403}{2016}$
