1×2分之x+2×3分之x+3×4分之x+...+2009×2010分之x=2009 求方程解

x/(1×2)+x/(2×3)+x/(3×4)...+x/(2009×2010)=2009x[1/(1×2)+1/(2×3)+1/(3×4)+...+1/(2009×2010)]=2009x/(1-1/2+1/2-1/3+1/3-1/4+...+1/2009-1/2010)=2009x/(1-1/2010)=20092009x/2010=2009x=2010