Iterating a Square-Root Expression
Iterating a Square-Root Expression
This Demonstration shows an iteration of the sequence =, starting with the initial value ≥-, ; the conditions avoid complex numbers. The sequence converges to for all permissible values of . The sequence is monotonically increasing, decreasing, or constant, according to whether , , or .
x
n+1
2a+b
x
n
x
0
b
2a
a,b≥0
L=a++b
2
a
x
0
L>
x
0
L<
x
0
L=
x
0