Question

1×2+3×4+5×6+……+999×1000 等于几?

Answer 1

1×2+3×4+5×6+……+999×1000

=(2²-2)+(4²-4)+(6²-6)+……+(1000²-1000)

=(2²+4²+6²+……+1000²)-(2+4+6+……+1000)

=4x(1²+2²+3²+……+500²)-(2+4+6+……+1000)

=4x500x501x1001/6-1002x500/2

=167167000+250500

=166916500