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2015 Argentina National Olympiad
1
sum of k(3k+1 ) / {(3k-1)(3k+2) as irreducible fraction
sum of k(3k+1 ) / {(3k-1)(3k+2) as irreducible fraction
Source: 2015 Argentina OMA Finals L3 p1
January 16, 2023
algebra
Sum
Problem Statement
Express the sum of
99
99
99
terms
1
⋅
4
2
⋅
5
+
2
⋅
7
5
⋅
8
+
…
+
k
(
3
k
+
1
)
(
3
k
−
1
)
(
3
k
+
2
)
+
…
+
99
⋅
298
296
⋅
299
\frac{1\cdot 4}{2\cdot 5}+\frac{2\cdot 7}{5\cdot 8}+\ldots +\frac{k(3k+1 )}{(3k-1)(3k+2)}+\ldots +\frac{99\cdot 298}{296\cdot 299}
2
⋅
5
1
⋅
4
+
5
⋅
8
2
⋅
7
+
…
+
(
3
k
−
1
)
(
3
k
+
2
)
k
(
3
k
+
1
)
+
…
+
296
⋅
299
99
⋅
298
as an irreducible fraction.
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