简便运算:(1-2x2/1)X(1-3x3/1)X(1-4x4/1)x……x(1-12x12/1)

题目

简便运算:(1-2x2/1)X(1-3x3/1)X(1-4x4/1)x……x(1-12x12/1)
急

答案

(1-2x2/1)+(1-3x3/1)+(1-4x4/1)……(1-12x12/1)

=(1+1+1+……+1)(11个1)-[(1^2+2^2+3^2+4^2+……+12^2)-1]
=12-(1^2+2^2+3^2+4^2+……+12^2)
=12-12×13×(2×12+1)/6            [n(n+1)(2n+1)/6]
=12-2×13×(2×12+1)
=12-2×13×25
=12-50×13
=12-650
=-638