Question

Find the limit of a(n) assuming that it converges

Answer 1

The sequence {a(n)} is defined by a(1)=2, and
\[a _{n+1}=\frac{ 1 }{2 }(a _{n}+\frac{ 2 }{ a _{n} })\]

Answer 2

for n>= 1 .

Answer 3

Let a=lim n→∞ a(n). Then, since a(n+1)=(1/2)(an+(2/an)), we have a=(1/2)(a+(2/a)). Now solve for a.