简便：（99^2+98^2+.+90^2）-（89^2-88^2+...+80^2）

[(100-1)^2+(100-2)^2+.+(100-10)^2]-[(100-11)^2+(100-12)^2+.+(100-20)^2]详细过程上式可转换为：（100^2-2x100x1+1^2+100^2-2x100x2+2^2+....+100^2-2x100x10+11^2)-（100^2-2x100x11+11^2+100^2-2x100x12+12^2+....+100^2-2x100x20+20^2)=21500也可以用另一种方法：原式=[(90+9)^2+(90+8)^2+....+(90+1)^2+90^2] - [(90-1)^2+(90-2)^2+....+(90-9)^2+(90-10)^2] =[(90+9)^2-(90-9)^2]+....+[(90+1)^2-(90-1)^2]+90^2-(90-10)^2 =(2x90x9x2+....+2x90x1x2)+2x90x10-10^2 =360x60-10^2 =21600-100 =21500