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Lebl-Basic-Analysis-I
· Problem 2.2.5
Sequences and Series
Mathematics · facts-about-limits-of-sequences
Problem
Let
x
n
:
=
n
−
cos
(
n
)
n
x_n := \dfrac{n - \cos(n)}{n}
x
n
:=
n
n
−
cos
(
n
)
. Use the squeeze lemma to show that
{
x
n
}
n
=
1
∞
\{x_n\}_{n=1}^\infty
{
x
n
}
n
=
1
∞
converges and find the limit.
Related theory
Sequences Convergence Cauchy Sequences Subsequences
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