Question
Find the unit digit of the expression: 1! + 2! + 3! +
4! + 5! + ........ + 999!.Solution
1! = 1 2! = 1 X 2 = 2 3! = 1 X 2 X 3 = 6 4! = 1 X 2 X 3 X 4 = 24 5! = 1 X 2 X 3 X 4 X 5 = 120 6! = 1 X 2 X 3 X 4 X 5 X 6 = 720 Here, we can observe that the unit-digit of numbers larger than 4! Is 0. So, unit digit of the given expression, 1! + 2! + 3! + 4! + 5! + ........ + 999! = unit digit of (1 + 2 + 6 + 4 + 0) = unit digit of 13 Required unit digit = 3
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