解：lim(n->∞)(1/(n+2）+1/(n+4)+.........+1/(n+2i)+....+1/(n+2n)) =lim(n->∞)[1/n((1+2*1/n)+1/(1+2*2/n)+...+1/(1+2*i/n)+...+1/(1+2*n/n))] =∫(0,1)dx/(1+2x) (应用积分定义) =[ln(1+2x)/2]|(0,1) =ln3-ln1 =ln3.
