1/1*6+1/6*11+1/11*16+1/16*21+....+1/71*76

Решите задачу:

$\frac{1}{1*6}+\frac{1}{6*11}+\frac{1}{11*16}+\frac{1}{16*21}+...+\frac{1}{71*76}=\\\\\frac{1}{5}*\frac{5}{1*6}+\frac{1}{5}*\frac{5}{6*11}+...+\frac{1}{5}*\frac{5}{71*76}=\\\\\frac{1}{5}(\frac{6-1}{1*6}+\frac{11-6}{6*11}+...+\frac{76-71}{71*76})=\\\\\frac{1}{5}*(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+...+\frac{1}{66}-\frac{1}{71}+\frac{1}{71}-\frac{1}{76})=\\\\\frac{1}{5}*(1-\frac{1}{76})=\frac{1}{5}*\frac{75}{76}=\frac{25}{76}$