Evalute the $\lim\limits_{n\to\infty} \frac{1}{n}\sum\limits_{k=0}^{\left \lfloor n/2\right \rfloor}\cos(\frac{k\pi}{n})$
122093
Limit involving cosine function
152557
Calculate $ \lim\limits_{n \to \infty} \sum\limits_{k=0}^n \frac{2^{k-1}}{a^{2k-1}+1} $
67500
Sum of $\lim_{n\rightarrow \infty}\left(\frac{n}{n^2+1}+\frac{n}{n^2+2}+\cdots \cdots \cdots +\frac{n}{n^2+n}\right)$
104996
Limit of $\lim_{n\rightarrow \infty} \sum^{n}_{i=1} \frac{1}{\sqrt {n^2 +i} }$
53537
Evaluate $\lim_{n\rightarrow\infty}\sum_{k=1}^n\arcsin(\frac k{n^2})$
5054
Calculate $\sum\limits_{k=0}^{\infty}\frac{1}{{2k \choose k}}$
107843
Convergence of the series $\sum\limits_{n=2}^{\infty} \frac{ (-1)^n} { \ln(n) +\cos(n)}$
5974
Evaluating $\lim\limits_{n\to\infty} e^{-n} \sum\limits_{k=0}^{n} \frac{n^k}{k!}$
154286
Evaluating $\lim_{n \to \infty} (1 + 1/n)^{n}$
40227
Compute $\lim\limits_{n\to\infty}n^2\left(\left(1+\frac1{n+1}\right)^{n+1}-\left(1+\frac1n\right)^n\right)$
106527
Limit of $(\cos1/n)^{n^2}$ when $n\to\infty$
132988
$ \lim_{n \to \infty} \left(\frac 1{n^2+1}+\frac 2{n^2+2}+\frac 3{n^2+3}+\cdots +\frac n{n^2+n}\right)$
106281
Prove $\lim\limits_{n\to \infty}\frac{1}{\sqrt n}\left|\sum\limits_{k=1}^n (-1)^k\sqrt k\right|= \frac{1}{2}$
117370
$\lim_{n\to\infty} \left(1+\frac{2}{n}\right)^{n^2} e^{-2n}$
79646
Compute $\lim_{n\to\infty}\frac{\tfrac{n}{1}+\tfrac{n-1}{2}+\dots+\tfrac{2}{n-1}+\tfrac{1}{n}}{\ln(n!)}$
5072
To evaluate limit of sequence $\left(\left( 1 + \frac1n \right) \left( 1 + \frac2n \right)\cdots\left( 1 + \frac nn \right) \right)^{1/n}$
49029
Find the limit $\lim_{n\rightarrow\infty}\sum_{k=1}^{n}\frac{1}{k+n}$