WOLFRAM|DEMONSTRATIONS PROJECT

Iterating a Square-Root Expression

​
a
1.5
b
4
initial value
x
0
0.3
iteration n
0
This Demonstration shows an iteration of the sequence
x
n+1
=
2a
x
n
+b
, starting with the initial value
x
0
≥-
b
2a
,
a,b≥0
; the conditions avoid complex numbers. The sequence converges to
L=a+
2
a
+b
for all permissible values of
x
0
. The sequence is monotonically increasing, decreasing, or constant, according to whether
L>
x
0
,
L<
x
0
, or
L=
x
0
.