MathDB
Ahsme 1999 #25

Source:

January 30, 2006
factorial

Problem Statement

There are unique integers a2,a3,a4,a5,a6,a7 a_2, a_3, a_4, a_5, a_6, a_7 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 0ai<i 0 \le a_i < 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=latexbold>(A)</span> 8<spanclass=latexbold>(B)</span> 9<spanclass=latexbold>(C)</span> 10<spanclass=latexbold>(D)</span> 11<spanclass=latexbold>(E)</span> 12 <span class='latex-bold'>(A)</span>\ 8 \qquad <span class='latex-bold'>(B)</span>\ 9 \qquad <span class='latex-bold'>(C)</span>\ 10 \qquad <span class='latex-bold'>(D)</span>\ 11 \qquad <span class='latex-bold'>(E)</span>\ 12