Is $\lim_{n\to\infty}\frac{p_{n+1}}{p_n}=1$ where $p_n$ is the $n$th prime number?
118023
Let $(p_n)_{n \in \mathbb{N}}$ be the sequence of prime numbers, then $\lim_{n \to \infty}\frac{p_{n+1}}{p_n} = 1$?
97747
Limit of $\lim\limits_{n\to\infty} (1 + \frac{x_n}{n})^n$
99752
how does one solve $\lim_{n\to \infty} (\frac{n^{2}-2n+1}{n^{2}-4n+2})^{n}$
17069
Limit $\lim_{x\to \infty} \frac{\sqrt{x+1}+\sqrt{x+2}-\sqrt{4x+12}}{\sqrt{x+2}+\sqrt{x}-\sqrt{4x+12}}$
114412
Limit $\lim_{n\to \infty} \frac{1}{2n} \log{2n\choose n}$
122990
How can I prove that $\lim\limits_{n\to\infty}\frac{n+\sin n}{n+1} = 1$
9541
Evaluate $\lim_{n\to\infty}\frac {qn+1}{qn} \frac {qn+p+1}{qn+p} \cdots \frac {qn+np+1}{qn+np}$ where $p\in\mathbb{N}\setminus\{0,1\},q>0.$
45737
Limit $\lim_{n \to \infty} \frac{n!}{n^n}$
49929
If $ \lim_{n \to \infty} (2 x_{n + 1} - x_{n}) = x $, then is it true that $ \lim_{n \to \infty} x_{n} = x $?
75581
Is the sum of the first $n$ primes a prime infinitely many times?
42841
Convergence of series involving the prime numbers
44857
Why the $(n+1)$th prime number cannot exceed the smallest prime divisor of $p_1\dotsc p_n + 1$
44551
What is the result of $ \lim_{n \to \infty} \frac{ \sum^n_{i=1} i^k}{n^{k+1}},\ k \in \mathbb{R} $ and why?
151701
Does there exist an $a_0$ such that the sequence $a_{n+1} = 2a_n + 1$ is prime for all $n \ge 0$?
78342
When is $\phi(n)$ a prime number?
61300
Evaluating $\lim\limits_{n\to\infty} \left(\frac{1^p+2^p+3^p + \cdots + n^p}{n^p} - \frac{n}{p+1}\right)$
63581
Computation of a limit involving factorial $\lim_{n \to \infty} \sqrt[n+1] {(n+1)!} - \sqrt[n] {(n)!} = \frac{1}{e}$