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Netherlands Contests
Dutch Mathematical Olympiad
1989 Dutch Mathematical Olympiad
3
sum1/ \sqrt{n+\sqrt{n^2-1}}}
sum1/ \sqrt{n+\sqrt{n^2-1}}}
Source: Netherlands - Dutch MO 1989 p3
December 25, 2022
Sum
algebra
Problem Statement
Calculate
∑
n
=
1
1989
1
n
+
n
2
−
1
\sum_{n=1}^{1989}\frac{1}{\sqrt{n+\sqrt{n^2-1}}}
n
=
1
∑
1989
n
+
n
2
−
1
1
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