(124+248+`````+n2n4n/136+2612+````+n3n6n)^2

来源：学生作业帮助网编辑：六六作业网时间：2024/11/16 01:16:13

(1*2*4+2*4*8+`````+n*2n*4n/1*3*6+2*6*12+````+n*3n*6n)^2(1*2*4+2*4*8+`````+n*2n*4n/1*3*6+2*6*12+````+

(1*2*4+2*4*8+`````+n*2n*4n/1*3*6+2*6*12+````+n*3n*6n)^2
(1*2*4+2*4*8+`````+n*2n*4n/1*3*6+2*6*12+````+n*3n*6n)^2

(1*2*4+2*4*8+`````+n*2n*4n/1*3*6+2*6*12+````+n*3n*6n)^2
∵1*2*4+2*4*8+`````+n*2n*4n=1*2*4(1+2^3+...+n^3)
1*3*6+2*6*12+````+n*3n*6n=1*3*6(1+2^3+...+n^3)
∴(1*2*4+2*4*8+`````+n*2n*4n/1*3*6+2*6*12+````+n*3n*6n)^2
=(1*2*4/1*3*6)^2
=16/81