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Putnam
1969 Putnam
B3
B3
Part of
1969 Putnam
Problems
(1)
Putnam 1969 B3
Source: Putnam 1969
3/31/2022
The terms of a sequence
(
T
n
)
(T_n)
(
T
n
)
satisfy
T
n
T
n
+
1
=
n
T_n T_{n+1} =n
T
n
T
n
+
1
=
n
for all positive integers
n
n
n
and
lim
n
→
∞
T
n
T
n
+
1
=
1.
\lim_{n\to \infty} \frac{ T_{n} }{ T_{n+1}}=1.
n
→
∞
lim
T
n
+
1
T
n
=
1.
Show that
π
T
1
2
=
2.
\pi T_{1}^{2}=2.
π
T
1
2
=
2.
Putnam
Sequences
pi