一道数学题（七年级有理数）计算1/(1*2)+1/(2*3)+1/(3*4)+1/(4*5)+...+1/(1999*2000)

一道数学题（七年级有理数）计算1/(1*2)+1/(2*3)+1/(3*4)+1/(4*5)+...+1/(1999*2000)
一道数学题（七年级有理数）
计算
1/(1*2)+1/(2*3)+1/(3*4)+1/(4*5)+...+1/(1999*2000)

一道数学题（七年级有理数）计算1/(1*2)+1/(2*3)+1/(3*4)+1/(4*5)+...+1/(1999*2000)
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+…+(1/1999-1/2000)
=1-1/2000
=1999/2000
其中1/n(n+1)=1/n-1/(n+1)

1/(1*2)+1/(2*3)+1/(3*4)+1/(4*5)+...+1/(1999*2000)
=1-1/2+1/2-1/3+)+...+1/1999-1/2000
=1-1/2000
=1999/2000