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Latvia BW TST
2017 Latvia Baltic Way TST
13
\sqrt{1 + 1/n^2 + 1/(n+1)^2} is rational
\sqrt{1 + 1/n^2 + 1/(n+1)^2} is rational
Source: 2017 Latvia BW TST P13
December 18, 2022
algebra
rational
radical
Problem Statement
Prove that the number
1
+
1
n
2
+
1
(
n
+
1
)
2
\sqrt{1 + \frac{1}{n^2} + \frac{1}{(n+1)^2}}
1
+
n
2
1
+
(
n
+
1
)
2
1
is rational for all natural
n
n
n
.
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