f(n)>0 for all n£N

Question

if f(n+1)=1/2( f(n)+(9/f(n)) ) , n€N and f(n)>0 for all n€N then find   lim n-infinity f(n) .

Answer 1

I cannot prove this to you, but the answer is 3.  The formula you have submitted is the Newton method for finding square root and in this case, the square root of 9.