[小尤]数学题

来源：百度知道 编辑：UC知道 时间：2024/05/14 14:39:23
数列{an},a1=1,对所有n>=2有a1*a2*a3*.......*an=n^2,则a5/a3=?
要过程!!忘说了!!

a1*a2*a3*a4*a5=5^2 。。。。。。。。。。。A
a1*a2*a3=3^2 ......................B
A/B得，a4*a5=(5/3)^2 ..........(1)
a1*a2=2^2 ......................C
a1*a2*a3*a4=4^2 ......................D
D/C得，a3*a4=(4/2)^2 ..........(2)
(1)/(2),得a5/a3=25/36

25/36

a5=5^2/4^2
a3=4^2/3^2
a5/a3=225/256

225/64

a2=4,4a3=9,a3=9/4,81a4=16,a4=16/9,16a5=25,a5=25/16
a5/a3=25/16*4/9=25/36
另解a1a2*……*an-1*an=(n-1)^2*an=n^2,an=(n/(n-1))^2
a5=(5/4)^2=25/16,a3=(3/2)^2=9/4,a5/a3=25/36