Question

计算1/2+1/(3x2)+1/(4x3)+.+1/(2011x2010)=?

Answer 1

1/2+1/(3x2)+1/(4x3)+.+1/(2011x2010)=1/2+1/2-1/3+1/3-1/4+……+1/2010-1/2011=1-1/2011=2010/2011