Question Number 80501 by naka3546 last updated on 03/Feb/20
$$\frac{\mathrm{5}}{\mathrm{7}}\:\:=\:\:\frac{{a}_{\mathrm{2}} }{\mathrm{2}!}\:+\:\frac{{a}_{\mathrm{3}} }{\mathrm{3}!}\:+\:\frac{{a}_{\mathrm{4}} }{\mathrm{4}!}\:+\:\frac{{a}_{\mathrm{5}} }{\mathrm{5}!}\:+\:\frac{{a}_{\mathrm{6}} }{\mathrm{6}!}\:+\:\frac{{a}_{\mathrm{7}} }{\mathrm{7}!} \\ $$$$\mathrm{0}\:\:\leqslant\:{a}_{{i}} \:<\:{i}\:\:,\:\:{a}_{{i}} \:\:\in\:\mathbb{N} \\ $$$${Find}\:\:{possible}\:\:{value}\:\:{of}\:\:\:{a}_{\mathrm{2}} \:+\:{a}_{\mathrm{3}} \:+\:{a}_{\mathrm{4}} \:+\:{a}_{\mathrm{5}} \:+\:{a}_{\mathrm{6}} \:+\:{a}_{\mathrm{7}} \:\:. \\ $$