Limit of sequence $ S_n $=$\int_0^1 \frac{nx^{n-1}}{1+x}dx $
11489
Limit of $s_n = \int\limits_0^1 \frac{nx^{n-1}}{1+x} dx$ as $n \to \infty$
33495
A limit problem about $a_{n+1}=a_n+\frac{n}{a_n}$
35325
Prove that $\lim_{n\to\infty}\frac1{n}\int_0^{n}xf(x)dx=0$.
143227
Show that: $\lim \limits_{n\to\infty}\frac{x_n-x_{n-1}}{n}=0 $
87338
Find the value of a given integral sequence: $I_n=\int_{0}^{1}(1-x^2)^ndx$
118023
Let $(p_n)_{n \in \mathbb{N}}$ be the sequence of prime numbers, then $\lim_{n \to \infty}\frac{p_{n+1}}{p_n} = 1$?
138052
How to work out the limit of  this bounded sequence?
6878
Prove limit of sequence
148492
Finding the limit of the sequence $(1 - 1/\sqrt 2) \dotsm ( 1 - 1/\sqrt {n+1})$
5072
To evaluate limit of sequence $\left(\left( 1 + \frac1n \right) \left( 1 + \frac2n \right)\cdots\left( 1 + \frac nn \right) \right)^{1/n}$
37906
Prove $s_n$ is a Cauchy sequence for $|s_{n+1}-s_n|\lt2^{-n}$
146663
Limit $\lim_{n \to \infty} \frac {a_n}{2^{n-1}}=\frac 4{\pi}$ for $a_{n+1}=a_n+\sqrt{1+a_n^2}$ and $a_0=0$
155475
$\lim\limits_{n\to \infty} \int_0^1 |f(x)-a_nx-b_n| dx=0$ implies $(a_n)_n,(b_n)_n$ are convergent
12031
Asymptotic behavior of the sequence $a_n=\sqrt{n+a_{n-1}}$
73812
Does $\lim \limits_ {n\to \infty}\ \frac{n}{n+1}$ equal $1$?
28669
Find limit of the following sequence: $\frac{\log(n+1)}{\log(n)}$?
107470
To show that the limit of the sequence $\sum\limits_{k=1}^n \frac{n}{n^2+k^2}$ is $\frac{\pi}{4}$