Question

数列{an}中,a1等于二分之一,a2等于四分之一,an+an+2+an*an+2等于一,则a5

Answer 1

a1=1/2,a2=1/4

an+a(n+2)+an*a(n+2)=1

那么(1+an)*a(n+2)=1-an

a(n+2)=(1-an)/(1+1an)

∴a3=(1-a1)/(1+a1)=(1-1/2)/(1+1/2)=1/3

a5=(1-a3)/(1+a3)=(1-1/3)/(1+1/3)=1/2

a4=(1-a2)/(1+a2)=(1-1/4)/(1+1/4)=3/5

a6=(1-a5)/(1+a5)=(1-3/5)/(1+3/5)=1/4

a5=1/2,a6=1/4