计算:﹣1×1/2+(﹣1/2×1/3)+(﹣1/3×1/4)+···(﹣1/2011×1/2012)

问题描述:

计算:﹣1×1/2+(﹣1/2×1/3)+(﹣1/3×1/4)+···(﹣1/2011×1/2012)

裂项法:
﹣1×1/2+(﹣1/2×1/3)+(﹣1/3×1/4)+···(﹣1/2011×1/2012)
=-1+1/2-1/2+1/3-1/3+1/4-……-1/2011+1/2012
=-1+1/2012
=-2011/2012