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Putnam
1957 Putnam
B2
B2
Part of
1957 Putnam
Problems
(1)
Putnam 1957 B2
Source: Putnam 1957
7/1/2022
In order to determine
1
A
\frac{1}{A}
A
1
for
A
>
0
A>0
A
>
0
, one can use the iteration
X
k
+
1
=
X
k
(
2
−
A
X
k
)
,
X_{k+1}=X_{k}(2-AX_{k}),
X
k
+
1
=
X
k
(
2
−
A
X
k
)
,
where
X
0
X_0
X
0
is a selected starting value. Find the limitation, if any, on the starting value
X
0
X_0
X
0
so that the above iteration converges to
1
A
.
\frac{1}{A}.
A
1
.
Putnam
iterated function
limit