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Lebl-Basic-Analysis-I
· Problem 2.2.3
Sequences and Series
Mathematics · facts-about-limits-of-sequences
Problem
Prove that if
{
x
n
}
n
=
1
∞
\{x_n\}_{n=1}^\infty
{
x
n
}
n
=
1
∞
is a convergent sequence,
k
∈
N
k \in \mathbb{N}
k
∈
N
, then
lim
n
→
∞
x
n
k
=
(
lim
n
→
∞
x
n
)
k
.
\lim_{n\to\infty} x_n^k = \left(\lim_{n\to\infty} x_n\right)^k.
n
→
∞
lim
x
n
k
=
(
n
→
∞
lim
x
n
)
k
.
Hint: Use induction.
Related theory
Sequences Convergence Cauchy Sequences Subsequences
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