2.设直线L1:y=kx+k-1和直线L2:y=(k+1)x+k (k为正整数)及 x轴围成的三角形面积为Sk,
问题描述:
2.设直线L1:y=kx+k-1和直线L2:y=(k+1)x+k (k为正整数)及 x轴围成的三角形面积为Sk,
2.设直线L1:y=kx+k-1和直线L2:y=(k+1)x+k
(k为正整数)及 x轴围成的三角形面积为Sk,
求S1+S2+S3+…….+S2011的值.
答
L1:y=kx+k-1与x轴交点:0=kx+k-1,x1=-(k-1)/kL2:y=(k+1)x+k与x轴交点:0=(k+1)x+k,x2=-k/(k+1)k为正整数,x1>x2L1与L2交点横坐标:kx+k-1=(k+1)x+k,x3=-1y3=-k+k-1=-1三角形面积S(k)=1/2(x1-x2)*|y3|=1/2[-(k-1)/k+k...