While not a rigorous proof, you could experiment with programing by calculating k_0 = sqrt(6) and k_n+1 = sqrt (6 + k_n) for successively higher values of n.

I think that you will find it converges pretty quickly to 3.

You can also determine the value for convergence algebraically by squaring both sides which results in k^2 = 6 + k and then solving the quadratic.

## Jerry-

2019-11-13

While not a rigorous proof, you could experiment with programing by calculating

`k_0 = sqrt(6)`

and`k_n+1 = sqrt (6 + k_n)`

for successively higher values of n.I think that you will find it converges pretty quickly to 3.

You can also determine the value for convergence algebraically by squaring both sides which results in

`k^2 = 6 + k`

and then solving the quadratic.