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