Compute $\lim\limits_{n\to\infty}(x_{n+1}-x_n)$ if $x_n =\sum\limits_{k=1}^{n-1}f(\frac kn)$ and $f$ continuous (but not continuously differentiable)
20431
Speed of convergence of Riemann sums
47381
If $\lim_{x\to\infty} [f(x+1)-f(x)] =l$ then $\lim_{ x\to\infty}f(x)/x =l$ ($f$ is continuous)
154286
Evaluating $\lim_{n \to \infty} (1 + 1/n)^{n}$
117497
Compute the limit $\lim_{n \to \infty} \frac{n!}{n^n}$
152557
Calculate $ \lim\limits_{n \to \infty} \sum\limits_{k=0}^n \frac{2^{k-1}}{a^{2k-1}+1} $
106527
Limit of $(\cos1/n)^{n^2}$ when $n\to\infty$
119145
$\lim\limits_{n\rightarrow\infty} \sqrt{n}(\sqrt{n+1}-\sqrt{n})$
90773
$\lim_{n\rightarrow\infty}\frac{1}{n}\sum_{k=1}^{n}\frac{k}{k^{2}+1}$
56902
Evaluate $\lim_{n \to \infty} \frac{1}{n}[(n +1)(n+2) \cdots (n+n)]^{\frac{1}{n}}$
26541
Is $\sum_{n=1}^{\infty}{\frac{\sin(nx)}n}$ continuous?
135877
$\lim\limits_{n \to \infty} \frac{a_n}{b_n}=l$ ; Prove $\sum\limits_{k=1}^\infty a_k$ converges iff $\sum\limits_{k=1}^\infty b_k$ converges.
9610
Find the sum of $\sum\limits_{n=1}^{\infty} \frac{x^{n}}{n(n+1)}$
44926
How do you calculate that $\lim_{n \to \infty} \sum_{k=1}^{n} \frac {n}{n^2+k^2} = \frac{\pi}{4}$?
149296
Is it trivial to say $\mathop {\lim }\limits_{n \to \infty } {(1 + {k \over n})^n} = e^{k}$
4643
The limit of truncated sums of harmonic series, $\lim\limits_{k\to\infty}\sum_{n=k+1}^{2k}{\frac{1}{n}}$
12914
What's the limit of the sequence $\lim\limits_{n \to\infty} \frac{n!}{n^n}$?
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 $k<p$