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A summation of integers close to square roots
A summation of integers close to square roots
Source: Germany 2004 - Problem
December 25, 2022
algebra
square roots
Sum
Integers
Problem Statement
For a positive integer
n
,
n,
n
,
let
a
n
a_n
a
n
be the integer closest to
n
.
\sqrt{n}.
n
.
Compute
1
a
1
+
1
a
2
+
⋯
+
1
a
2004
.
\frac{1}{a_1 } + \frac{1}{a_2 }+ \cdots + \frac{1}{a_{2004}}.
a
1
1
+
a
2
1
+
⋯
+
a
2004
1
.
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