1乘2分之x+2乘3分之x+3乘4分之x+.+2009乘2010分之x
=X(1/(1*2)+1/(2*3)+...+1/(2009*2010))
=X*((1-1/2)+(1/2-1/3)+.+(1/2009-1/2010))
=X(1-1/2010)=2009X/2010=2009
==>X=2010