$\lim a^{b_n}=a^b$ if $\lim b_n = b$
74835
how to prove that $ \lim x_n^{y_n}=\lim x_n^{\lim y_n}$?
7507
Proof that $\lim{a_n}=L$ when $n$ goes to infinity, then $\{a_n\}$ its a Cauchy Sequence
11961
Why does $\lim_{n \to\infty}a_{n+1} = \lim_{n\to\infty}a_n$?
11834
Prove that $\liminf x_n = -\limsup (-x_n)$
123253
Limit of a sequence $a_1=1;a_{n+1}=(n+1)(1+a_n)$
17375
When is the limit of a sum equal to the sum of limits?
107764
Limit series $(a^n-b^n)^{1/n}$
104602
asymptotic of $x^{x^x} = n$
156541
$a^b > b^a$ or $a^b b$ where $a,b$ are positive real numbers
115411
if $A_n \longrightarrow \infty $ and $B_n \longrightarrow \infty $ then $(A_n+B_n) \longrightarrow \infty$
3111
How to prove that if $\lim_{n \rightarrow \infty}a_n=A$, then $\lim_{n \rightarrow \infty}\frac{a_1+...+a_n}{n}=A$
101268
if $|a|<1$ so $\lim_{n\to \infty}na^n=0$.
68700
Proving Two Limits Are Equal to Each Other
142778
Finding $\lim_{n\to\infty}a_n$ if $a_0=a,a_1=b$ and $a_n=\frac{1}{2}(a_{n-1}+a_{n-2})$ where $a, b \in \mathbb{R}$
47606
Proving $\lim_{n\to\infty} a^{\frac{1}{n}}=1$ by definition of limit
64654
Suppose $a, b$ and $n$ are positive integers. Prove that $a^n$ divides $b^n$ if and only if $a$ divides $b$.
76527
If $x_{m+n} \le x_n+x_m$, then $\lim x_n/n$ exists and is equal to $\inf x_n/n$