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Putnam
1950 Putnam
A3
A3
Part of
1950 Putnam
Problems
(1)
Putnam 1950 A3
Source:
5/24/2022
The sequence
x
0
,
x
1
,
x
2
,
…
x_0, x_1, x_2, \ldots
x
0
,
x
1
,
x
2
,
…
is defined by the conditions
x
0
=
a
,
x
1
=
b
,
x
n
+
1
=
x
n
−
1
+
(
2
n
−
1
)
x
n
2
n
x_0 = a, x_1 = b, x_{n+1} = \frac{x_{n - 1} + (2n - 1) ~x_n}{2n}
x
0
=
a
,
x
1
=
b
,
x
n
+
1
=
2
n
x
n
−
1
+
(
2
n
−
1
)
x
n
for
n
≥
1
,
n \ge 1,
n
≥
1
,
where
a
a
a
and
b
b
b
are given numbers. Express
lim
n
→
∞
x
n
\lim_{n \to \infty} x_n
lim
n
→
∞
x
n
concisely in terms of
a
a
a
and
b
.
b.
b
.
Putnam