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Costa Rica - Final Round
2016 Costa Rica - Final Round
A1
sum ...+1/(\sqrt{2015}+\sqrt{2016}) OLCOMA Costa Rica Final 2016 Shortlist A1 D1
sum ...+1/(\sqrt{2015}+\sqrt{2016}) OLCOMA Costa Rica Final 2016 Shortlist A1 D1
Source:
September 23, 2021
algebra
Problem Statement
Prove that
(
1
1
+
2
+
1
2
+
3
+
1
3
+
4
+
.
.
.
+
1
2015
+
2016
)
2
(
2017
+
24
14
)
=
201
5
2
\left( \frac{1}{\sqrt1+\sqrt2}+\frac{1}{\sqrt2+\sqrt3}+\frac{1}{\sqrt3+\sqrt4}+...+\frac{1}{\sqrt{2015}+\sqrt{2016}}\right)^2(2017+24\sqrt{14})=2015^2
(
1
+
2
1
+
2
+
3
1
+
3
+
4
1
+
...
+
2015
+
2016
1
)
2
(
2017
+
24
14
)
=
201
5
2
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