Why does $\lim_{n \to \infty} x^{1+1/(2n-1)}=|x|$?
43829
Limit of $h_n(x)=x^{1+\frac{1}{2n-1}}$
80373
How to prove that $\lim_{n \to\infty} \frac{(2n-1)!!}{(2n)!!}=0$
49929
If $ \lim_{n \to \infty} (2 x_{n + 1} - x_{n}) = x $, then is it true that $ \lim_{n \to \infty} x_{n} = x $?
136602
Why is $\int_1^{\infty}(1/x^2)\,dx$  less than $\sum_{n=1}^{\infty} 1/(n^2)$?
123576
Why does $\lim_{n\to\infty} z_n=A$ imply $\lim_{n\to\infty}\frac{1}{n}(z_1+\cdots+z_n)=A$?
25206
How to prove that $\lim\limits_{n\to \infty}a_{n+1}=\lim\limits_{n\to \infty}a_{n}$
47895
Prove $\lim\limits_{n\to\infty}n^{-1/(p+1)}(1^{1^p}\cdot 2^{2^p}\cdots n^{n^p})^{n^{-p-1}}=e^{-1/(p+1)^2}$
86843
Find the value of : $\lim_{n\to\infty}[(n+1)\int_{0}^{1}x^{n}\ln(1+x)dx]$.
108917
Use $\delta-\epsilon$ to show that $\lim_{n\to\infty} a^{\frac{1}{n}} = 1$?
64001
What is the result of $\lim\limits_{x \to 0}(1/x - 1/\sin x)$?
135155
Why is $\lim_{n \to +\infty }{\sqrt[n]{a_1 a_2 \cdots a_n}} =\lim_{n \to +\infty}{a_n}$
72693
Prove: $\lim_{x\to\infty}x^{2/3}((x+1)^{1/3}-x^{1/3})=1/3$
66441
Prove that $|x|<1$ implies that $\lim_{n \to \infty} x^n=0$
36060
If $\lim_{n\to\infty}x_n=\alpha$, show $\lim_{n\to\infty}(x_1x_2\dots x_n)^{1/n} =\alpha$.
73812
Does $\lim \limits_ {n\to \infty}\ \frac{n}{n+1}$ equal $1$?
105064
What is wrong with this fake proof that $\lim\limits_{n\rightarrow \infty}\sqrt[n]{n!} = 1$?
9781
How to prove that $\lim_{n \to \infty} n x^{n} = 0 $ when $0<x<1$?