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Putnam
1954 Putnam
B7
B7
Part of
1954 Putnam
Problems
(1)
Putnam 1954 B7
Source: Putnam 1954
7/17/2022
Let
a
>
0
a>0
a
>
0
. Show that
lim
n
→
∞
∑
s
=
1
n
(
a
+
s
n
)
n
\lim_{n \to \infty} \sum_{s=1}^{n} \left( \frac{a+s}{n} \right)^{n}
n
→
∞
lim
s
=
1
∑
n
(
n
a
+
s
)
n
lies between
e
a
e^a
e
a
and
e
a
+
1
.
e^{a+1}.
e
a
+
1
.
Putnam
limit
exponential