1/(1×2)+1/(2×3)+1/(3×4)+……+1/(19×20)+1/(20×21)=?答案上是20/21,_数学解答

1/(1×2)+1/(2×3)+1/(3×4)+……+1/(19×20)+1/(20×21)=?
答案上是20/21,

人气：194 ℃　时间：2020-06-06 07:54:31

解答

1/(1×2)+1/(2×3)+1/(3×4)+……+1/(19×20)+1/(20×21)
=1-1/2+1/2-1/3+1/3-1/4+……+1/19-1/20+1/20-1/21
=1-1/21
=20/21