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Lebl-Basic-Analysis-I
· Problem 2.4.6
Sequences and Series
Mathematics · cauchy-sequences
Problem
Suppose
∣
x
n
−
x
k
∣
≤
n
/
k
2
|x_n - x_k| \leq n/k^2
∣
x
n
−
x
k
∣
≤
n
/
k
2
for all
n
n
n
and
k
k
k
. Show that
{
x
n
}
n
=
1
∞
\{x_n\}_{n=1}^\infty
{
x
n
}
n
=
1
∞
is Cauchy.
Related theory
Sequences Convergence Cauchy Sequences Subsequences
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