这是小学六年级数学题还是有点难度!

xfhaoym

这是小学六年级数学题,对他们来说还是有点难度!

S=1/3+1/6+1/10+...........+1/45=?

如果延伸一下,有无限多项S=?

王守恩

S=1/3+1/6+1/10+1/15+1/21+1/28+1/36+1/45
  =2×(1/(2×3)+1/(3×4)+1/(4×5)+1/(5×6)+1/(6×7)+1/(7×8)+1/(8×9)+1/(9×10))
  =2×(1/2 -1/3+1/3-1/4+1/4 -1/5+1/5-1/6+1/6 -1/7+1/7-1/8+1/8 -1/9+1/9 -1/10)
  =2×(1/2 -1/10)=4/5