Reminder after dividing factorial 1! + 2! + 3! + ? + 100! By 7?

(a + b + c + d + .... x ) / 7 = a/7 + b/7 + c/7 + .... x / 7 Therefore 1!+2!+..100! / 7 = 1!/7 + .. 7!/7 + ..100! / 7 Reminder of (a+b)/7 = Reminder(Reminder (a/7) + Reminder (b/7)) / 7 Since Reminder of all numbers from 7! to 100! are 0 , Reminder of 1!+..100! is 1!+2!+3!+..6! = 1 + 2 + 6 + 24 + 120 + 720 = 873 Reminder of 873 divided by 7 is 5

Hence Answer : 5

20 Feb, 2010
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