Question

(1-2x2/1)+(1-3x3/1)+(1-4x4/1)……(1-2001x2001/1)=?要过程

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