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Putnam
1987 Putnam
B4
B4
Part of
1987 Putnam
Problems
(1)
Putnam 1987 B4
Source:
8/5/2019
Let
(
x
1
,
y
1
)
=
(
0.8
,
0.6
)
(x_1,y_1) = (0.8, 0.6)
(
x
1
,
y
1
)
=
(
0.8
,
0.6
)
and let
x
n
+
1
=
x
n
cos
y
n
−
y
n
sin
y
n
x_{n+1} = x_n \cos y_n - y_n \sin y_n
x
n
+
1
=
x
n
cos
y
n
−
y
n
sin
y
n
and
y
n
+
1
=
x
n
sin
y
n
+
y
n
cos
y
n
y_{n+1}= x_n \sin y_n + y_n \cos y_n
y
n
+
1
=
x
n
sin
y
n
+
y
n
cos
y
n
for
n
=
1
,
2
,
3
,
…
n=1,2,3,\dots
n
=
1
,
2
,
3
,
…
. For each of
lim
n
→
∞
x
n
\lim_{n\to \infty} x_n
lim
n
→
∞
x
n
and
lim
n
→
∞
y
n
\lim_{n \to \infty} y_n
lim
n
→
∞
y
n
, prove that the limit exists and find it or prove that the limit does not exist.
Putnam