If a (n) = a(n-1) / a(n-1)-1,a (1)=8,which of the following is a (501)?A 8 B 7/8 C 1/8 D 8/7 E 4

If a (n) = a(n-1) / a(n-1)-1,a (1)=8,which of the following is a (501)?A 8 B 7/8 C 1/8 D 8/7 E 4
If a (n) = a(n-1) / a(n-1)-1,a (1)=8,which of the following is a (501)?
A 8 B 7/8 C 1/8 D 8/7 E 4

If a (n) = a(n-1) / a(n-1)-1,a (1)=8,which of the following is a (501)?A 8 B 7/8 C 1/8 D 8/7 E 4
a(n)=a(n-1)/a(n-1)-1 = [a(n-1)-1]+1/a(n-1)-1 = 1+1/a(n-1)-1
a(n)-1=1/a(n-1)-1
令b(n)=a(n)-1 b(n)=1/b(n-1)
所以b(n+1)=1/b(n)=b(n-1)
所以b(501)=b(499)=……=b(1)
b(1)=a(1)-1=8-1=7
b(501)=7=a(501)-1 a(501)=8
选A