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National and Regional Contests
Moldova Contests
JBMO TST - Moldova
2023 Junior Balkan Team Selection Tests - Moldova
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1
Part of
2023 Junior Balkan Team Selection Tests - Moldova
Problems
(1)
\frac{1}{n\cdot(\sqrt{n+1}+\sqrt{n})+\sqrt{n}}
Source: Moldova JTST 2023
5/5/2023
The positive integer
n
n
n
verifies
1
1
⋅
(
2
+
1
)
+
1
+
1
2
⋅
(
3
+
2
)
+
2
+
⋯
+
1
n
⋅
(
n
+
1
+
n
)
+
n
=
2022
2023
.
\frac{1}{1\cdot(\sqrt{2}+\sqrt{1})+\sqrt{1}}+\frac{1}{2\cdot(\sqrt{3}+\sqrt{2})+\sqrt{2}}+\cdots+\frac{1}{n\cdot(\sqrt{n+1}+\sqrt{n})+\sqrt{n}}=\frac{2022}{2023}.
1
⋅
(
2
+
1
)
+
1
1
+
2
⋅
(
3
+
2
)
+
2
1
+
⋯
+
n
⋅
(
n
+
1
+
n
)
+
n
1
=
2023
2022
.
Find the sum of digits of number
n
n
n
.
Number theor