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Contests
National and Regional Contests
Iran Contests
Pre-Preparation Course Examination
2011 Pre-Preparation Course Examination
4
calculating the sum
calculating the sum
Source:
February 26, 2011
geometry
advanced fields
advanced fields unsolved
Problem Statement
represent a way to calculate
∑
k
=
0
∞
(
−
1
)
k
(
2
k
+
1
)
3
=
1
−
1
3
3
+
1
5
3
−
1
7
3
+
.
.
.
\sum_{k=0}^{\infty}\frac{(-1)^k}{(2k+1)^3}=1-\frac{1}{3^3}+\frac{1}{5^3}-\frac{1}{7^3}+...
∑
k
=
0
∞
(
2
k
+
1
)
3
(
−
1
)
k
=
1
−
3
3
1
+
5
3
1
−
7
3
1
+
...
.
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