1×2分之1+2×3分之1+3×4分之1+.+19×20分之1等于?_数学解答

1×2分之1+2×3分之1+3×4分之1+.+19×20分之1等于?

人气：440 ℃　时间：2019-10-20 00:01:52

解答

1/(1×2)+1/(2×3)+.+1/(19+20)
=(1/1-1/2)+(1/2-1/3)+.+(1/19-1/20)
=1/1-1/2+1/2-1/3+1/3-.-1/19+1/19-1/20
=1-1/2+1/2-1/3+1/3-.-1/19+1/19-1/20
=1-1/20
=19/20