Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Mathematics
Mathematics
Problem
Let
f
:
N
→
R
f: \mathbb{N} \to \mathbb{R}
f
:
N
→
R
be such that
f
(
1
)
=
1
f(1) = 1
f
(
1
)
=
1
and
f
(
1
)
+
2
f
(
2
)
+
3
f
(
3
)
+
⋯
+
n
f
(
n
)
=
n
(
n
+
1
)
f
(
n
)
,
for
n
≥
2
f(1) + 2f(2) + 3f(3) + \dots + nf(n) = n(n+1)f(n), \text{ for } n \ge 2
f
(
1
)
+
2
f
(
2
)
+
3
f
(
3
)
+
⋯
+
n
f
(
n
)
=
n
(
n
+
1
)
f
(
n
)
,
for
n
≥
2
then
1
2010
f
(
2010
)
is
…
…
…
…
…
\text{then } \frac{1}{2010 f(2010)} \text{ is } \dots\dots\dots\dots\dots
then
2010
f
(
2010
)
1
is
……………
Browse the problem library