Evaluate $ \lim_{n\to+\infty}\frac{1}{n}\sum_{k=1}^n\Big[\frac{2n}{k}\Big]-2\Big[\frac{n}{k}\Big]$.
41974
Limit of Series with differences of Floor function
152557
Calculate $ \lim\limits_{n \to \infty} \sum\limits_{k=0}^n \frac{2^{k-1}}{a^{2k-1}+1} $
155873
Evaluate $\lim\limits_{n\rightarrow \infty}\frac{n+n^2+n^3+\cdots +n^n}{1^n+2^n+3^n+\cdots +n^n}.$
49029
Find the limit $\lim_{n\rightarrow\infty}\sum_{k=1}^{n}\frac{1}{k+n}$
156546
Evaluate the limit $\lim_{n\rightarrow \infty}\frac{1}{\sqrt{n}}\left(1+\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}+\ldots+\frac{1}{\sqrt{n}}\right)$
56961
Evaluate the limit of $\sum_{n=1}^{\infty}\frac{n^2}{n!}$
37059
limit of the sum $\frac{1}{n+1}+\frac{1}{n+2}+\cdots+\frac{1}{2n} $
50334
What is $\lim_{n \rightarrow \infty}\sum\limits_{k = 1}^n\frac{k}{n^2}$?
8387
Evaluate $\lim_{n \rightarrow \infty} \frac {[(n+1)(n+2)\cdots(n+n)]^{1/n}}{n}$
125497
Evaluating $\lim_{n \to \infty} n\left(1-\frac{1}{e}\left(1+\frac{1}{n}\right)^{n} \right)$
106281
Prove $\lim\limits_{n\to \infty}\frac{1}{\sqrt n}\left|\sum\limits_{k=1}^n (-1)^k\sqrt k\right|= \frac{1}{2}$
17872
Evaluate $\lim\limits_{n\to\infty}\frac{\sum_{k=1}^n k^m}{n^{m+1}}$
4578
Evaluate the value of $\lim_{n \to \infty}\frac{x_n}{\prod_{i=1}^{n-1} x_i}$ where $x_n=x_{n-1}^2-2, x_1=5$
84147
Evaluating $\sum_{n=1}^\infty \frac{2^{2n-1}}{5^{n+1}}$
61698
Evaluate the limit $\lim\limits_{n \to \infty} \frac{1}{1+n^2} +\frac{2}{2+n^2}+ \ldots +\frac{n}{n+n^2}$
49262
Evaluation of Sum of $ \sum_{n=1}^{\infty}\frac{\sin (n)}{n}$.
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?