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Lebl-Basic-Analysis-I
· Problem 2.2.7
Sequences and Series
Mathematics · facts-about-limits-of-sequences
Problem
True or false, prove or find a counterexample. If
{
x
n
}
n
=
1
∞
\{x_n\}_{n=1}^\infty
{
x
n
}
n
=
1
∞
is a sequence such that
{
x
n
2
}
n
=
1
∞
\{x_n^2\}_{n=1}^\infty
{
x
n
2
}
n
=
1
∞
converges, then
{
x
n
}
n
=
1
∞
\{x_n\}_{n=1}^\infty
{
x
n
}
n
=
1
∞
converges.
Related theory
Sequences Convergence Cauchy Sequences Subsequences
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