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7
R 7
R 7
Source:
May 25, 2007
limit
calculus
integration
geometry
3D geometry
inequalities
triangle inequality
Problem Statement
Show that the number
r
(
n
)
r(n)
r
(
n
)
of representations of
n
n
n
as a sum of two squares has
π
\pi
π
as arithmetic mean, that is
lim
n
→
∞
1
n
∑
m
=
1
n
r
(
m
)
=
π
.
\lim_{n \to \infty}\frac{1}{n}\sum^{n}_{m=1}r(m) = \pi.
n
→
∞
lim
n
1
m
=
1
∑
n
r
(
m
)
=
π
.
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