x/(1*3)+x/(3*5)+.+x/(2008*2010)=2009
x/2*(1-1/3)+x/2*(1/3-1/5)+……+x/2*(1/2008-1/2010)=2009
x/2*(1-1/3+1/3-1/5+……+1/2008-1/2010)=2009
x/2*(1-1/2010)=2009
x/2*2009/2010=2010
x=2*2010
x=4020
x/(1*3)+x/(3*5)+.+x/(2008*2010)=2009
x/2*(1-1/3)+x/2*(1/3-1/5)+……+x/2*(1/2008-1/2010)=2009
x/2*(1-1/3+1/3-1/5+……+1/2008-1/2010)=2009
x/2*(1-1/2010)=2009
x/2*2009/2010=2010
x=2*2010
x=4020