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Question 124

The remainder obtained when $$1! + 2! + 3! + .... + (2014)!$$ is divided by 7 is

Solution

The remainder will actually depend on the sum from 1!+2!+3!+4!+...........+6! because after that every factorial will be a multiple of 7. This sums up to 873. Hence the sum will be 7m+873. Now 873 when divided by 7, has remainder 5. Hence the remainder will be 5.

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