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Lebl-Basic-Analysis-I
· Problem 2.4.7
Sequences and Series
Mathematics · cauchy-sequences
Problem
Suppose
{
x
n
}
n
=
1
∞
\{x_n\}_{n=1}^\infty
{
x
n
}
n
=
1
∞
is a Cauchy sequence such that for infinitely many
n
n
n
,
x
n
=
c
x_n = c
x
n
=
c
. Using only the definition of Cauchy sequence prove that
lim
n
→
∞
x
n
=
c
\lim_{n\to\infty} x_n = c
lim
n
→
∞
x
n
=
c
.
Related theory
Sequences Convergence Cauchy Sequences Subsequences
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