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Let be a function from the set of positive integers to the set of real numbers such…
MATHEMATICS · Subjective · AoPS · Mathematics · Functions · Functions
Problem
Let
f
f
f
be a function from the set of positive integers to the set of real numbers such that
f
(
1
)
=
1
f(1)=1
f
(
1
)
=
1
and
∑
r
=
1
n
r
f
(
r
)
=
n
(
n
+
1
)
f
(
n
)
,
∀
n
≥
2
,
\sum_{r=1}^{n} r f(r) = n(n+1)f(n), \ \forall n \ge 2,
r
=
1
∑
n
r
f
(
r
)
=
n
(
n
+
1
)
f
(
n
)
,
∀
n
≥
2
,
the value of
f
(
1063
)
f(1063)
f
(
1063
)
is .....
Related theory
Special Series
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