Evaluate: $\lim_{n\to\infty}\frac{\sum_{k=1}^n\lfloor kx\rfloor}{n^2}$
124426
Help in evaluating: $\lim_{n \to \infty} \frac{\sum_{k=1}^n\lfloor kx\rfloor}{n^2} $
94678
Evaluate $\sum\limits_{n=1}^{\infty} \frac{1}{2^n}\tan\frac{x}{2^n}$
56365
Evaluate $\sum\limits_{k=1}^{n} \frac{k}{2^k}$
6838
Evaluate the series $S_n = \sum_{k=1}^n\log\frac {k (k + 2)}{(k + 1)^2}$
71798
$\lim_{n\to \infty}\frac{1}{n} \sum_{k=1}^n x_k =x\;$ given $\;\lim_{n\to \infty} x_n= x\;?$
79646
Compute $\lim_{n\to\infty}\frac{\tfrac{n}{1}+\tfrac{n-1}{2}+\dots+\tfrac{2}{n-1}+\tfrac{1}{n}}{\ln(n!)}$
89263
Find the limit $\lim_{n \to \infty} \sum_{k=1}^n \frac{1}{k+n}$
42519
$\lim_{n \rightarrow \infty} \sum^n_{k=1} \frac{1}{k+n}$
20843
Evaluate the limit of $\lim_{n\to\infty}\frac{1}{n^2}\left(\frac{2}{1}+\frac{9}{2}+\frac{64}{9}+\cdots+\frac{(n+1)^{n}}{n^{n-1}}\right)$
50334
What is $\lim_{n \rightarrow \infty}\sum\limits_{k = 1}^n\frac{k}{n^2}$?
145154
Calculating limit of $\sum_{k = 0}^\infty \frac{n^k}{k!} \vert k - n \vert$
65137
Evaluating $\lim\limits_{n\to\infty}(a_1^n+\dots+a_k^n)^{1\over n}$ where $a_1 \ge \cdots\ge a_k \ge 0$
81654
Evaluate $\lim_{n\to\infty} [{1\over kn}+{1\over k(n+1)}+{1\over k(n+2)}+\cdots+{1\over k(n+p-k)}]$ where $k<p$
76828
Evaluating $\sum_{i = 0}^{\lfloor n/2 \rfloor} {n \choose 2i}p^{2i}(1 - p)^{n - 2i}$
28461
Show that $\lim_{n\to\infty} \sum_{k=1}^{n} \frac{n}{n^2+k^2}=\frac{\pi}{4}$
84147
Evaluating $\sum_{n=1}^\infty \frac{2^{2n-1}}{5^{n+1}}$
56961
Evaluate the limit of $\sum_{n=1}^{\infty}\frac{n^2}{n!}$