(1!×1+2!×2+3!×3+...+2013!×2013)÷2014 余数为多少?
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![(1!×1+2!×2+3!×3+...+2013!×2013)÷2014 余数为多少?](/uploads/image/z/943972-52-2.jpg?t=%EF%BC%881%21%C3%971%2B2%21%C3%972%2B3%21%C3%973%2B...%2B2013%21%C3%972013%EF%BC%89%C3%B72014+%E4%BD%99%E6%95%B0%E4%B8%BA%E5%A4%9A%E5%B0%91%3F)
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(1!×1+2!×2+3!×3+...+2013!×2013)÷2014 余数为多少?
(1!×1+2!×2+3!×3+...+2013!×2013)÷2014 余数为多少?
(1!×1+2!×2+3!×3+...+2013!×2013)÷2014 余数为多少?
(1!×1+2!×2+3!×3+...+2013!×2013)
=(1!×2+2!×3+3!×4+...+2013!×2014)- (1!+2!+3!+...+2013!)
= (2!+3!+...+2013!+2014!)- (1!+2!+3!+...+2013!)
= 2014!- 1!
= 2014!-1
所以余数为-1,或2013
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