f(x)=2+1/x,数列an中a1=a,a(n+1)=f(an).设数列{bn}满足b1=-1/2,bn=f(b),且b10=a,问n为啥时,an=0?

Question

f(x)=2+1/x,数列an中a1=a,a( n+1)=f(an).设数列{bn}满足b1=-1/2,bn=f(b),且b10=a,问n为啥时,an=0?

Answer 1

根据题意有
a(n+1)=2+1/a(n)
b(n)=2+1/b(n+1)
故有
b(9)=2+1/b(10)
a(2)=2+1/a(1)
因为a(1)=a=b(10)
故b(9)=a(2)
同理b(8)=a(3)
b(7)=a(4)
……
b(1)=a(10)=-1/2
故a(11)=2+1/a(10)=2+(-2)=0
即当n=11时,a(n)=0