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Lebl-Basic-Analysis-I
· Problem 2.1.13
Sequences and Series
Mathematics · sequences-and-limits
Problem
Let
{
x
n
}
n
=
1
∞
\{x_n\}_{n=1}^\infty
{
x
n
}
n
=
1
∞
be a convergent monotone sequence. Suppose there exists a
k
∈
N
k \in \mathbb{N}
k
∈
N
such that
lim
n
→
∞
x
n
=
x
k
.
\lim_{n\to\infty} x_n = x_k.
n
→
∞
lim
x
n
=
x
k
.
Show that
x
n
=
x
k
x_n = x_k
x
n
=
x
k
for all
n
≥
k
n \geq k
n
≥
k
.
Related theory
sequences-and-limits
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