(1-2x2/1)+(1-3x3/1)+(1-4x4/1)……(1-2001x2001/1)=?要过程答案和过程都要

Question

(1-2x2/1)+(1-3x3/1)+(1-4x4/1)……(1-2001x2001/1)=?要过程
答案和过程都要

Answer 1

(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