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Lebl-Basic-Analysis-I
· Problem 2.1.19
Sequences and Series
Mathematics · sequences-and-limits
Problem
(Easy) Let
{
x
n
}
n
=
1
∞
\{x_n\}_{n=1}^\infty
{
x
n
}
n
=
1
∞
be a sequence and
x
∈
R
x \in \mathbb{R}
x
∈
R
such that there exists a
k
∈
N
k \in \mathbb{N}
k
∈
N
such that for all
n
≥
k
n \geq k
n
≥
k
,
x
n
=
x
x_n = x
x
n
=
x
. Prove that
{
x
n
}
n
=
1
∞
\{x_n\}_{n=1}^\infty
{
x
n
}
n
=
1
∞
converges to
x
x
x
.
Related theory
sequences-and-limits
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