Question

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

Answer 1

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