Question

a1=2 an+1/an=n/n+1 求an 为什么数列{nan}是各项均等于2的常数数列.

Answer 1

把an移到右边,a(n+1)=(nan)/(n+1)

用n-1代入上式的n处,an=[(n-1)/n]*a(n-1)

=[(n-1)/n]*[(n-2)/(n-1)]*[(n-3)/(n-2)]*.*[(2-1)/2]*a(2-1)

=[(n-1)/n]*[(n-2)/(n-1)]*[(n-3)/(n-2)]*.*1/2*a1

=1/n*a1=a1/n=2/n

故nan=2

{nan}是各项均等于2的常数数列.