若数列an满足a1=1,an+1/an=n/n+1,a8=

Question

若数列an满足 a1=1,an+1/an=n/n+1,a8=

Answer 1

a(n+1)/an=n/n+1
(a8/a7)×(a7/a6)×(a6/a5)×(a5/a4)×(a4/a3)×(a3/a2)×(a2/a1)
=a8/a1
=7/8×6/7×5/6×4/5×3/4×2/3×1/2
=1/8
a8/a1=1/8
a8=1/8
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