1/（1×2）+1/（2×3）+1/（3×4）+········+1/（9998×9999）+1/（9999×10000）
=(1-1/2)+(1/2- 1/3)+(1/3-1/4)+········+(1/9998-1/9999)+(1/9999-1/10000)
=1-1/2+1/2- 1/3+1/3-1/4+········+1/9998-1/9999+1/9999-1/10000
=1-1/10000
=9999/10000
先根据题中的1-1/2=1/（1×2）；1/2- 1/3=1/（2×3）······,把算式展开.后面就可以吧中间抵消,就好算了,呵呵