$\lim_{n \to \infty} \frac1n \sum_{r=1}^n r^{\frac1r}$
29901
Computing $\lim_{n\rightarrow \infty} \frac{1+\sqrt{2}+\sqrt[3]{3}+\cdots+\sqrt[n]{n}}{n}$.
47606
Proving $\lim_{n\to\infty} a^{\frac{1}{n}}=1$ by definition of limit
157539
Prove: $\lim\limits_{n\to\infty}\frac{1}{n}\sum\limits_{k=1}^{n}\sqrt{1+\frac{k}{n}}=\frac{2}{3}(2\sqrt{2}-1)$
11389
What is $\lim_{n\to \infty}\sum_{k=1}^n \left(\frac{k}{n}\right)^n$?
102414
$\lim_{n \to \infty} (\frac{(n+1)(n+2)\dots(3n)}{n^{2n}})^{\frac{1}{n}}$ is equal to :
49128
How to prove $\lim\limits_{n \to \infty} (1+\frac1n)^n = e$?
97571
Find the limit $ \lim_{n\to \infty} 2^{\frac{1}{n}}$
73812
Does $\lim \limits_ {n\to \infty}\ \frac{n}{n+1}$ equal $1$?
49029
Find the limit $\lim_{n\rightarrow\infty}\sum_{k=1}^{n}\frac{1}{k+n}$
54775
Find $\lim_{n \to \infty} n[(1+\frac{1}{n})^n - e]$
89698
Please help with $\sum\limits_{r=1}^{N}\frac{2r+3}{3^r(r+1)}$
143227
Show that: $\lim \limits_{n\to\infty}\frac{x_n-x_{n-1}}{n}=0 $
73865
Find $\lim_{n\to\infty}n\left(\sum_{i=1}^{n}\dfrac{1}{(n+i)^2}\right)$
99752
how does one solve $\lim_{n\to \infty} (\frac{n^{2}-2n+1}{n^{2}-4n+2})^{n}$
135700
Show that $\lim_{n \to \infty} (1/n)\sum_{i=1}^n f(x_i)$ exists
106028
Sum of $\frac{1}{(2n)(2n+1)}$ from $1$ to infinity
71240
The limit of a sum $\sum_{k=1}^n \frac{n}{n^2+k^2}$ as $n\rightarrow\infty$