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Problem
Problem
If
f
(
x
+
y
+
z
)
=
f
(
x
)
+
f
(
y
)
+
f
(
z
)
f(x+y+z) = f(x) + f(y) + f(z)
f
(
x
+
y
+
z
)
=
f
(
x
)
+
f
(
y
)
+
f
(
z
)
with
f
(
1
)
=
1
f(1) = 1
f
(
1
)
=
1
and
f
(
2
)
=
2
f(2) = 2
f
(
2
)
=
2
and
x
,
y
,
z
∈
R
x, y, z \in \mathbb{R}
x
,
y
,
z
∈
R
, the value of
lim
n
→
∞
∑
r
=
1
n
(
4
r
)
f
(
3
r
)
n
3
\lim_{n \to \infty} \sum_{r=1}^{n} \frac{(4r)f(3r)}{n^3}
lim
n
→
∞
∑
r
=
1
n
n
3
(
4
r
)
f
(
3
r
)
is .....
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