数列an中,a1=1,a1a2……an=n²,求a3+a5

题目

数列an中,a1=1,a1a2……an=n²,求a3+a5

答案

a1*a2*a3*……*an=n^2 (1)
a1*a2*a3*……*an-1=(n-1)^2 (2)
(1)除以(2),得an=[n/(n-1)]^2
a3=(3/2)^2=9/4
a5=(5/4)^2=25/16
a3+a6=61/16