Limit of the sequence $a_n = \frac{1+\sqrt2+\sqrt 3+ \cdots +\sqrt n}{n\sqrt n}$
20773
Find $\lim\limits_{n \to \infty} \frac{\sqrt 1 + \sqrt 2 + \dots + \sqrt{n}}{n\sqrt{n}}$.
113172
Please show me how to calculate the folowing limit of a sequence
113891
The limit of a sum of the form $a_0 \sqrt n + a_1 \sqrt {n + 1} +\cdots + a_k \sqrt {n + k}$
69717
Find limit of recursive sequence $a_{n+1} =\sqrt{2+ \sqrt{a_n} }.$
104456
Show that $\lim_{n\to\infty}b_n=\frac{\sqrt{b^2-a^2}}{\arccos\frac{a}{b}}$
74629
Find the limit of the sequence $\{\frac{x_1 + 2x_2 + ... + nx_n}{n^2}\}$, where $\{x_n\}$ is a convergent sequence in a normed space S.
8773
Finding $\lim\limits_{n \to \infty}{\frac{1^1+2^2+3^3+\cdots+n^n}{n^n}}$
5072
To evaluate limit of sequence $\left(\left( 1 + \frac1n \right) \left( 1 + \frac2n \right)\cdots\left( 1 + \frac nn \right) \right)^{1/n}$
76932
How to show $\lim_{n \to \infty} a_n = \frac{ [x] + [2x] + [3x] + \dotsb + [nx] }{n^2} = x/2$?
95095
$x_{n+m}\le \frac{x_n+x_{n+1}+\cdots+x_{n+m-1}}{m}$. Prove that this sequence has a limit.
146663
Limit $\lim_{n \to \infty} \frac {a_n}{2^{n-1}}=\frac 4{\pi}$ for $a_{n+1}=a_n+\sqrt{1+a_n^2}$ and $a_0=0$
62937
Test for the convergence of the sequence $S_n =\frac1n \left(1 + \frac{1}{2} + \frac{1}{3} + \cdots+ \frac{1}{n}\right)$
5797
Limit of the sequence $a_n=\sqrt[n+1]{(n+1)!}-\sqrt[n]{n!}$
4345
Prove that lim $(\sqrt{n^2+n}-n) = \frac{1}{2}$
107470
To show that the limit of the sequence $\sum\limits_{k=1}^n \frac{n}{n^2+k^2}$ is $\frac{\pi}{4}$
158960
How to find limit of the sequence $\sum\limits_{k=1}^n\frac{1}{\sqrt {n^2 +kn}}$?
12031
Asymptotic behavior of the sequence $a_n=\sqrt{n+a_{n-1}}$