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2005 Greece Junior Math Olympiad
2
Evaluate sum
Evaluate sum
Source: 22nd Hellenic Jounior mo , 2005 , prb2.
November 17, 2005
Problem Statement
If
f
(
n
)
=
2
n
+
1
+
n
(
n
+
1
)
n
+
1
+
n
f(n)=\frac{2n+1+\sqrt{n(n+1)}}{\sqrt{n+1}+\sqrt{n}}
f
(
n
)
=
n
+
1
+
n
2
n
+
1
+
n
(
n
+
1
)
for all positive integers
n
n
n
, evaluate (a)
f
(
1
)
f(1)
f
(
1
)
, (b) the sum
A
=
f
(
1
)
+
f
(
2
)
+
.
.
.
+
f
(
400
)
A=f(1)+f(2)+...+f(400)
A
=
f
(
1
)
+
f
(
2
)
+
...
+
f
(
400
)
.
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