请教小学六年级数学脱式计算(1/2)/(1+1/2)+(1/3)

请教小学六年级数学脱式计算(1/2)/(1+1/2)+(1/3): 脱式计算 (1/2)/(1+1/2)+(1/3)/(1+1/2)*(1+1/3)+(1/4)/(1+1/2)*(1+1/3)*(1+1/4)+...+(1/2000)/(1+1/2)*(1+1/3)+(1/4)/(1+1/2)*(1+1/3)*(1+1/4)*...*(1+1/2000); 第(n-1)项式子为：(1/n)/(1+1/2)*...*(1+1/n) 分子分母同乘以(2*3*...*n)得[2*3*...*(n-1)]/[3*4*...*(n+1)] 化简为2/[n*(n+1)] 而1/[n*(n+1)]为[1/n - 1/(n+1)] 故1到第1999项即n从2到2000的和经相邻项前后抵消后为：2(1/2 - 1/2001) = 1999/2001