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National and Regional Contests
Greece Contests
Greece JBMO TST
2003 Greece JBMO TST
2
sum ...+ \sqrt{1+\frac{1}{(n-1)^2}+\frac{1}{n^2}}
sum ...+ \sqrt{1+\frac{1}{(n-1)^2}+\frac{1}{n^2}}
Source: Greece JBMO TST 2003 p2
June 18, 2019
Sum
algebra
Problem Statement
Calculate if
n
∈
N
n\in N
n
∈
N
with
n
>
2
n>2
n
>
2
the value of
B
=
1
+
1
2
2
+
1
3
2
+
1
+
1
3
2
+
1
4
2
+
.
.
.
+
1
+
1
(
n
−
1
)
2
+
1
n
2
B=\sqrt{1+\frac{1}{2^2}+\frac{1}{3^2}}+\sqrt{1+\frac{1}{3^2}+\frac{1}{4^2}}+...+\sqrt{1+\frac{1}{(n-1)^2}+\frac{1}{n^2}}
B
=
1
+
2
2
1
+
3
2
1
+
1
+
3
2
1
+
4
2
1
+
...
+
1
+
(
n
−
1
)
2
1
+
n
2
1
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