数学题1/4x1/5x1/6+1/5x1/6x1/7+1/6x1/7x1/8+.+1/98×1/99×1/100=? 谢
2个回答

1/4x1/5x1/6=1/5x(1/4x1/6)=1/5x[1/2x(1/4-1/6)]=1/2x(1/4x1/5-1/5x1/6)

同样得到1/5x1/6x1/7=1/2x(1/5x1/6-1/6x1/7)

……

1/98×1/99×1/100=1/2x(1/98x1/99-1/99x1/100)

所以原式=1/2x(1/4x1/5-1/5x1/6+1/5x1/6-1/6x1/7+……+1/98x1/99-1/99x1/100)

=1/2x(1/4x1/5-1/99x1/100)=1/2x(1/20-1/9900)=1/2x494/9900=247/9900