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Putnam
1960 Putnam
B5
B5
Part of
1960 Putnam
Problems
(1)
Putnam 1960 B5
Source: Putnam 1960
6/11/2022
Define a sequence
(
a
n
)
(a_n)
(
a
n
)
by
a
0
=
0
a_0 =0
a
0
=
0
and
a
n
=
1
+
sin
(
a
n
−
1
−
1
)
a_n = 1 +\sin(a_{n-1}-1)
a
n
=
1
+
sin
(
a
n
−
1
−
1
)
for
n
≥
1
n\geq 1
n
≥
1
. Evaluate
lim
n
→
∞
1
n
∑
k
=
1
n
a
k
.
\lim_{n\to \infty} \frac{1}{n} \sum_{k=1}^{n} a_k.
n
→
∞
lim
n
1
k
=
1
∑
n
a
k
.
Putnam
Sequence
limit