1/1*2+1/2*3+1/3*4+......1/2010*2011=1-1/2+1/2-1/3+1/3-1/4+……+1/2010-1/2011=1-1/2011=2010/2011
1/1*2+1/2*3+1/3*4+......1/2010*2011=1-1/2+1/2-1/3+……+1/2010-1/2011=1-1/2011=2010/2011