Question

1乘2分之+2乘3分之1+3乘4分之1+……+2011乘2012分之1等于几?

Answer 1

1/2-1/3=1/6=1/ 2*1/3 1/3-1/4=1/12=1/3*1/4.1/n-1/(n+1)=1/[n(n+1)]=1/n*1/(n+1)1/(1x2)+1/(2x3)+1/(3x4)+.+1/(2011x2012)=1-1/2+1/2-1/3+1/3-1/4+.+1/2011-1/2012=1-1/2012=2011/2012原式=1/2乘以（1-1/3+1/3-1/5+...