Calculate limit using Riemann integral/Riemann sum
50243
Find $\lim_{n \to +\infty} \frac{1}{n}\sqrt[n]{\frac{(2n)!}{n!}} $ using Riemann integral
150971
If $f$ is Riemann integrable on $[0,1]$ then $\lim\limits_{n\rightarrow\infty}\frac{1}{n}\sum f\left(\frac{k}{n}\right)=\int\limits_{0}^{1} f(x)dx$
1234
Evaluating limits of integrals
5054
Calculate $\sum\limits_{k=0}^{\infty}\frac{1}{{2k \choose k}}$
109059
Evaluate $\lim\limits_{n\to \infty}\frac{1}{n+1}+\frac{1}{n+2}+\cdots+\frac{1}{6n}$
49489
Compute $\lim_{n\to\infty} \int_{0}^{\pi/4}\tan^n x \ dx$
44926
How do you calculate that $\lim_{n \to \infty} \sum_{k=1}^{n} \frac {n}{n^2+k^2} = \frac{\pi}{4}$?
37378
Is a function with limits Riemann integrable?
31866
Calculating the limit $\lim((n!)^{1/n})$
49928
Proving limit of a sum
94189
Calculate the limit including binomial coefficients
17438
Evaluate $\lim_{n\to \infty} \sum_{r=1}^n \frac {1}{2^r}\tan \left(\frac {1}{2^r}\right)$
4224
Evaluate limit of an integral: $\lim_{x\to \infty }\frac{1}{x}\int _0^x\:\frac{dt}{2+\cos t}$
76560
How do I calculate this limit: $\lim\limits_{n\to\infty}1+\sqrt[2]{2+\sqrt[3]{3+\dotsb+\sqrt[n]n}}$?
17674
Riemann Lower Sum by definition
17332
How to compute $\sum\limits_{n=1}^{\infty}\frac{1}{x^n-1}$?
123675
Evaluate the following limit of finite sum