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Question
If (1*1! + 2*2! + 3*3! +...+63*63!) is divided by 64, find the remainder.
If (1*1! + 2*2! + 3*3! +...+63*63!) is divided by 64, find the remainder.
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Solution
The correct option is C 63
The above series can be written as (2-1)*1! + (3-1)*2! + (4-1) 3! +...+(64-1)*63!
= 2! - 1! + 3! - 2! + 4! - 3! +.....+ 64! - 63!
= 64! - 1!
Therefore the remainder is (-1) or 63.
63
The above series can be written as (2-1)*1! + (3-1)*2! + (4-1) 3! +...+(64-1)*63!
= 2! - 1! + 3! - 2! + 4! - 3! +.....+ 64! - 63!
= 64! - 1!
Therefore the remainder is (-1) or 63.
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