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IMO Longlists
1976 IMO Longlists
10
10
Part of
1976 IMO Longlists
Problems
(1)
Writing reciprocal of 2(m^2+m+1) as sum of consecutive terms
Source:
1/3/2011
Show that the reciprocal of any number of the form
2
(
m
2
+
m
+
1
)
2(m^2+m+1)
2
(
m
2
+
m
+
1
)
, where
m
m
m
is a positive integer, can be represented as a sum of consecutive terms in the sequence
(
a
j
)
j
=
1
∞
(a_j)_{j=1}^{\infty}
(
a
j
)
j
=
1
∞
a
j
=
1
j
(
j
+
1
)
(
j
+
2
)
a_j = \frac{1}{j(j + 1)(j + 2)}
a
j
=
j
(
j
+
1
)
(
j
+
2
)
1
number theory unsolved
number theory