则左下半侧n-1条总面积为:
(1*n2+1*n-13-12)/2+(2*n2+2*n-23-22)/2+(3*n2+3*n-33-32)/2+…+[(n-1)*n2+(n-1)*n-(n-1)3-(n-1)2]/2 ={[1+2+3+…+(n-1)]n2+[1+2+3+…+(n-1)]n-[13+23+33+…+(n-1)3]-[12+22+32+…+(n-1)2]}/2
=[n(n-1)/2*n2+n(n-1)/2*n-(13+23+33+…+n3)+n3-(12+22+32+…+n2)+n2]/2
=[n3(n-1)/2+n2(n-1)/2-(13+23+33+…+n3)-(12+22+32+…+n2)+n3+n2]/2
为方便书写,记12+22+32+…+n2=t2,13+23+33+…+n3=t3
两侧全部空余部分面积为:
n3(n-1)/2+n2(n-1)/2-t3-t2+n^3+n^2=(n4+2n3+n2)/2-t3-t2