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Putnam
1940 Putnam
A7
A7
Part of
1940 Putnam
Problems
(1)
Putnam 1940 A7
Source: Putnam 1940
2/22/2022
If
∑
i
=
1
∞
u
i
2
\sum_{i=1}^{\infty} u_{i}^{2}
∑
i
=
1
∞
u
i
2
and
∑
i
=
1
∞
v
i
2
\sum_{i=1}^{\infty} v_{i}^{2}
∑
i
=
1
∞
v
i
2
are convergent series of real numbers, prove that
∑
i
=
1
∞
(
u
i
−
v
i
)
p
\sum_{i=1}^{\infty}(u_{i}-v_{i})^{p}
i
=
1
∑
∞
(
u
i
−
v
i
)
p
is convergent, where
p
≥
2
p\geq 2
p
≥
2
is an integer.
Putnam
Convergence