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8
2016-2017 Fall OMO Problem 8
2016-2017 Fall OMO Problem 8
Source:
November 16, 2016
Problem Statement
For a positive integer
n
n
n
, define the
n
n
n
th triangular number
T
n
T_n
T
n
to be
n
(
n
+
1
)
2
\frac{n(n+1)}{2}
2
n
(
n
+
1
)
, and define the
n
n
n
th square number
S
n
S_n
S
n
to be
n
2
n^2
n
2
. Find the value of
S
62
+
T
63
S
61
+
T
62
⋯
S
2
+
T
3
S
1
+
T
2
.
\sqrt{S_{62}+T_{63}\sqrt{S_{61}+T_{62}\sqrt{\cdots \sqrt{S_2+T_3\sqrt{S_1+T_2}}}}}.
S
62
+
T
63
S
61
+
T
62
⋯
S
2
+
T
3
S
1
+
T
2
.
Proposed by Yannick Yao
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