Problem Statement
There are unique integers a2,a3,a4,a5,a6,a7 such that \frac {5}{7} \equal{} \frac {a_2}{2!} \plus{} \frac {a_3}{3!} \plus{} \frac {a_4}{4!} \plus{} \frac {a_5}{5!} \plus{} \frac {a_6}{6!} \plus{} \frac {a_7}{7!}, where 0≤ai<i for i \equal{} 2,3...,7. Find a_2 \plus{} a_3 \plus{} a_4 \plus{} a_5 \plus{} a_6 \plus{} a_7.<spanclass=′latex−bold′>(A)</span> 8<spanclass=′latex−bold′>(B)</span> 9<spanclass=′latex−bold′>(C)</span> 10<spanclass=′latex−bold′>(D)</span> 11<spanclass=′latex−bold′>(E)</span> 12