Question

{an} a1=a+1/a(a>0 a不为1) An+1=a1-1/an 猜想数列通向 并用数学归纳法证明

Answer 1

a2=a1-1/a1=a+1/a-1/[a+1/a]=(a^4+a^2+1)/(a^2+1) *1/a=

a3=...=(a^6+a^4+a^2+1)/(a^4+a^2+1) *1/a

a4=...=(a^8+a^6+a^4+a^2+1)/(a^6+a^4+a^2+1) *1/a

设bn=a^2n+a^2(n-1)+...+a^2+1=1*[1-a^2(n+1)]/(1-a^2)

猜测an=bn/b(n-1) *1/a

n