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(1-2x2/1)+(1-3x3/1)+(1-4x4/1)……(1-2001x2001/1)=?要过程答案和过程都要
题目详情
(1-2x2/1)+(1-3x3/1)+(1-4x4/1)……(1-2001x2001/1)=?要过程
答案和过程都要
答案和过程都要
▼优质解答
答案和解析
(1-2x2/1)+(1-3x3/1)+(1-4x4/1)……(1-2001x2001/1)
=(1+1+1+……+1)(2001个1)-[(1^2+2^2+3^2+4^2+……+2001^2)-1]
=2002-(1^2+2^2+3^2+4^2+……+2001^2)
=2002-2001×2002×(2×2001+1)/6
=2002-2672671001
=-2672668999
=(1+1+1+……+1)(2001个1)-[(1^2+2^2+3^2+4^2+……+2001^2)-1]
=2002-(1^2+2^2+3^2+4^2+……+2001^2)
=2002-2001×2002×(2×2001+1)/6
=2002-2672671001
=-2672668999
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