Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Lebl-Basic-Analysis-I
· Problem 2.1.22
Sequences and Series
Mathematics · sequences-and-limits
Problem
Suppose that
{
x
n
}
n
=
1
∞
\{x_n\}_{n=1}^\infty
{
x
n
}
n
=
1
∞
is a sequence such that the subsequences
{
x
2
n
}
n
=
1
∞
\{x_{2n}\}_{n=1}^\infty
{
x
2
n
}
n
=
1
∞
,
{
x
2
n
−
1
}
n
=
1
∞
\{x_{2n-1}\}_{n=1}^\infty
{
x
2
n
−
1
}
n
=
1
∞
, and
{
x
3
n
}
n
=
1
∞
\{x_{3n}\}_{n=1}^\infty
{
x
3
n
}
n
=
1
∞
all converge. Show that
{
x
n
}
n
=
1
∞
\{x_n\}_{n=1}^\infty
{
x
n
}
n
=
1
∞
is convergent.
Related theory
sequences-and-limits
Browse the problem library