x/1*2+ x/2*3+ ...+x/2010*2011=2010
x(1/1*2+ 1/2*3+ ...+1/2010*2011)=2010
x(1-1/2+12-1/3+.+1/2010-1/2011)=2010
x(1-1/2011)=2010
2010x/2011=2010
x/2011=1
x=2011
x/1*2+ x/2*3+ ...+x/2010*2011=2010
x(1/1*2+ 1/2*3+ ...+1/2010*2011)=2010
x(1-1/2+12-1/3+.+1/2010-1/2011)=2010
x(1-1/2011)=2010
2010x/2011=2010
x/2011=1
x=2011