x/1*2+ x/2*3+ ...+x/2010*2011=2010x(1/1*2+ 1/2*3+ ...+1/2010*2011)=2010x(1-1/2+12-1/3+.+1/2010-1/2011)=2010x(1-1/2011)=20102010x/2011=2010x/2011=1x=2011为什么要减？通分1/1*2=1/2=1-1/21/2*3=1/6=1/2-1/3..............1/2010*1/2011=1/2010-1/2011