Is the limit $ \lim_{n\to \infty}\left(\sum^{n}_{r=0} \binom{n}{r}\big/{n^{r}(r+3)}\right)$ rational or irrational?
5521
Evalute $ \lim_{n\rightarrow \infty}\sum^{n}_{k=0}\frac{\binom{n}{k}}{n^k(k+3)} $
82831
Evaluating the limit $\lim_{n\to\infty} \left[ \frac{n}{n^2+1}+ \frac{n}{n^2+2^2} + \ldots + \frac{n}{n^2+n^2} \right]$
63617
Evaluating limit $\lim_{k\to \infty}\prod_{r=1}^k\cos{\left(\frac {x}{2^r}\right)}$
105971
Convergence of $\sum \limits_{n=1}^{\infty}\sqrt{n^3+1}-\sqrt{n^3-1}$
35439
Does the series $\;\sum\limits_{n=0}^{\infty}\left(\frac{\pi}{2} - \arctan(n)\right)$ converge or diverge?
89698
Please help with $\sum\limits_{r=1}^{N}\frac{2r+3}{3^r(r+1)}$
144403
Limit $\lim_{x\rightarrow +\infty}\sqrt{x}e^{-x}\left(\sum_{k=1}^{\infty}\frac{x^{k}}{k!\sqrt{k}}\right)$
107953
Limit of the sequence $\lim_{n\rightarrow\infty}\sqrt[n]n$
104878
What is the limit $\lim\limits_{n \to \infty} \frac{n^{\sqrt{n}}}{2^n}$?
73865
Find $\lim_{n\to\infty}n\left(\sum_{i=1}^{n}\dfrac{1}{(n+i)^2}\right)$
76638
Find the limit $ \lim_{n \to \infty}\left(\frac{a^{1/n}+b^{1/n}+c^{1/n}}{3}\right)^n$
89814
Limit of a Piecewise Function defined on Rationals and Irrationals
1760
Limit of the geometric sequence $\{r^n\}$, with $|r| < 1$, is $0$?
61487
Limit of $\frac1n\sqrt[n]{(n+1)(n+2)(n+3)...(n+n)}$
6815
$\lim_{n \rightarrow\infty} ~ x_{n+1} - x_n= c , c > 0$ . Then, is $\{x_n/n\}$ convergent?
142708
Finding the limit $\lim_{n\rightarrow\infty}(1-\frac{1}{3})^2(1-\frac{1}{6})^2(1-\frac{1}{10})^2...(1-\frac{1}{n(n+1)/2})^2$
17329
How do I find this limit: $\lim_{n\to\infty} \left[ n-{n\over e}\left(1+{1\over n}\right)^n \right]$?