What is the units digit of 1! + 2! + 3! + ... + 99! + 100!?

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Solution

The correct option is A 3
All numbers starting with 5! will end in zero. Therefore, Units digit of 1! + 2! + 3! + 4! + 5! + 6! ... + 100! is the same as units digit of (1! + 2! + 3! + 4!)
= 1 + 2 + 6 + 24 = 33. Hence , 3 is the answer.

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2 \times 3 \times 4 \times . . . \times 99

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S_{n} = {(4)}^{n} + 3

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