MathDB
Problems
Contests
Undergraduate contests
Miklós Schweitzer
1959 Miklós Schweitzer
7
7
Part of
1959 Miklós Schweitzer
Problems
(1)
Miklós Schweitzer 1959- Problem 7
Source:
11/8/2015
7. Let
(
z
n
)
n
=
1
∞
(z_n)_{n=1}^{\infty}
(
z
n
)
n
=
1
∞
be a sequence of complex numbers tending to zero. Prove that there exists a sequence
(
ϵ
n
)
n
=
1
∞
(\epsilon_n)_{n=1}^{\infty}
(
ϵ
n
)
n
=
1
∞
(where
ϵ
n
=
+
1
\epsilon_n = +1
ϵ
n
=
+
1
or
−
1
-1
−
1
) such that the series
∑
n
=
1
∞
ϵ
n
z
n
\sum_{n=1}^{\infty} \epsilon_n z_n
∑
n
=
1
∞
ϵ
n
z
n
is convergente. (F. 9)
complex numbers
college contests
real analysis