Answer
Convergent to $\approx 1.414$
Work Step by Step
We are given the sequence:
$a_{n+1}=\dfrac{1}{2}\left(a_n+\dfrac{2}{a_n}\right)$
$a_0=2$
Using a calculator, we get the values for $a_n$ when n=0,1,2,...,5.
$a_0=2$
$a_1=1.5$
$a_2=1.4166667$
$a_3=1.4142157$
$a_4=1.4142136$
$a_5=1.4142136$
We notice that the sequence is convergent and its limit is approximately 1.414.