(-1×1/2)+(-1/2×1/3)+(1/3×1/4)+…+(-1/2011×1/2012)+(-1/2012×1/2013)=?

来源：学生作业帮助网 编辑：作业帮 时间：2024/05/06 02:02:16
(-1×1/2)+(-1/2×1/3)+(1/3×1/4)+…+(-1/2011×1/2012)+(-1/2012×1/2013)=?

(-1×1/2)+(-1/2×1/3)+(1/3×1/4)+…+(-1/2011×1/2012)+(-1/2012×1/2013)=?
(-1×1/2)+(-1/2×1/3)+(1/3×1/4)+…+(-1/2011×1/2012)+(-1/2012×1/2013)=?

(-1×1/2)+(-1/2×1/3)+(1/3×1/4)+…+(-1/2011×1/2012)+(-1/2012×1/2013)=?
(-1×1/2)+(-1/2×1/3)+(1/3×1/4)+…+(-1/2011×1/2012)+(-1/2012×1/2013)
=（1/2-1）+（1/3-1/2）+（1/4-1/3）+（1/5-1/4）+（1/6-1/5）+.+（1/2013-1/2012）
=-1+1/2+1/3-1/2+1/4-1/3+1/5-1/4+1/6-1/5+.1/2013-1/2012(消除正负对应的数)
=-1+1/2013
=-2012/2013