左式＝x[1/(1*2)+1/(2*3)+…+1/(2008*2009)]
＝x[(1－1/2)+(1/2-1/3)+(1/3-1/4)+…+(1/2008-1/2009)]
=x(1-1/2009)＝右式＝2008
x＝2009