Convergence of a Recursive Sequence
Convergence of a Recursive Sequence
The limit of the sequence , or equivalently =1,=1+, satisfies the equation . The solutions are ,. In the graphic we show that the limit is the golden ratio .
1,1+,1+,1+,…
1
1
1
1+
1
1
1
1+
1
1+
1
1
a
1
a
n+1
1
a
n
x=1+
1
x
1+
5
2
1-
5
2
1+
5
2