x/1×2+x/2×3+x/3×4+……x/2008×2009=2008.求x的值.
问题描述：
x/1×2+x/2×3+x/3×4+……x/2008×2009=2008.求x的值.
答
左侧=x/(1×2)+x/(2×3)+x/(3×4)+……x/(2008×2009)
=x*(1/1-1/2) +x*(1/2-1/3) + x*(1/3-1/4)+...+x*(1/2008-1/2009)
=x*(1/1-1/2 + 1/2-1/3+ 1/3-1/4+...+1/2008-1/2009)
=x*(1/1-1/2009)
=x*2008/2009 = 右侧=2008
所以 x=2009
答
答：
原方程即：
x[1/(1*2)+1/(2*3)+...+1/(2008*2009)]=2008
x[(1/1-1/2)+(1/2-1/3)+...+(1/2008-1/2009)]=2008
x(1-1/2009)=2008
x*2008/2009=2008
x=2009