5/7=a2/2!+a3/3!+a4/4!+a5/5!+a6/6!+a7/7!
given that 0<=ai<i
find all the unknown terms. i could do this question using trial and error but it isn't very nice. any ingenious methods out there?
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5/7=a2/2!+a3/3!+a4/4!+a5/5!+a6/6!+a7/7!
given that 0<=ai<i
find all the unknown terms. i could do this question using trial and error but it isn't very nice. any ingenious methods out there?
(2520*a2 + 840*a3 +210*a4 + 42*a5 + 7*a6 + a7) /7! =5/7 (put whole side over 7!)
=> (2520*a2 + 840*a3 +210*a4 + 42*a5 + 7*a6 + a7) = 5*7!/7
=>(2520*a2 + 840*a3 +210*a4 + 42*a5 + 7*a6 + a7) = 3600
and easy from there
ai= i! 5/7 % i
a2=1
a3=1
a4=1
a5=0
a6=4
a7=2