计算:(1*2+2*3)*(1/1*2+1/2*3)+(2*3+3*4)*(1/2*3+1/3*4)+……+(19*20+20*21)*(1/19*20+1/20*21)=____________
问题描述：
计算:(1*2+2*3)*(1/1*2+1/2*3)+(2*3+3*4)*(1/2*3+1/3*4)+……+(19*20+20*21)*(1/19*20+1/20*21)=____________
答
第n项 [n*(n+1)+(n+1)*(n+2)]*[1/n*(n+1)+1/(n+1)*(n+2)]=1+(n+2)/n+n/(n+2)+1=4+2*[1/n-1/(n+2)]于是,上述和等于4*19+2*(1/1-1/3+1/2-1/4+1/3-1/6+...+1/18-1/20+1/19-1/21)=76+(1+1/2-1/20-1/21)=76+589/420...