Question

已知数列｛an｝各项均为正数,且Sn=1/2（an+1/an）,求an

Answer 1

Sn=1/2(an+1/an)

S(n-1)=Sn-an=1/2(1/an-an)

Sn+S(n-1)=1/an

Sn-S(n-1)=an

Sn^2-S(n-1)^2=1

S1=a1=1/2(a1+1/a1),a1=1

{Sn^2}是首项为S1^2=1,公差为1的等差数列

Sn^2=n

Sn=√n

an=Sn-S(n-1)=√n-√(n-1)