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National High School Mathematics League
2000 National High School Mathematics League
13
A Lot of Numbers
A Lot of Numbers
Source: 2000 National High School Mathematics League, Exam One, Problem 13
March 11, 2020
Problem Statement
Let
S
n
=
1
+
2
+
⋯
+
n
S_n=1+2+\cdots+n
S
n
=
1
+
2
+
⋯
+
n
for
n
∈
N
n\in\mathbb{N}
n
∈
N
, find the maximum value of
f
(
n
)
=
S
n
(
n
+
32
)
S
n
+
1
f(n)=\frac{S_n}{(n+32)S_{n+1}}
f
(
n
)
=
(
n
+
32
)
S
n
+
1
S
n
.
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