Question

（1*1+3*3+... +99*99）-（2*2+4*4+... +100*100）怎么算?

Answer 1

(1X1+3X3+...+99X99)-(2X2+4X4+...+100X100)

=(1X1-2X2)+(3X3-4X4)+...+(99X99-100X100)

=(1+2)(1-2)+(3+4)(3-4)+...+(99+100)(99-100)

=(1+2)(-1)+(3+4)(-1)+...+(99+100)(-1)

=-(1+2+3+4+...+100)

=-[(1+100)X100]÷2

=-5050