Proving that the limit of $\root n \of {{a_1}^n + {a_2}^n + ... + {a_k}^n}$ is $\max(a_1,...a_k)$
10383
The $ l^{\infty} $-norm is equal to the limit of the $ l^{p} $-norms.
30834
limit of $\lim\limits_{x \to \infty}((x+1)^a - x^a)$
143900
how can be prove that $\max(f(n),g(n)) = \Theta(f(n)+g(n))$
122800
Let $a > 0$ and let $k \in \mathbb{N}$. Evaluate the limit
47606
Proving $\lim_{n\to\infty} a^{\frac{1}{n}}=1$ by definition of limit
118244
An $n$th root inequality: $\sqrt[n]{n} < 1 + \sqrt{2/n}$
68913
Proving that $1_{\limsup A_n}=\limsup1_{A_n}$.
31836
Proof of $\lim_{n\to \infty} \sqrt[n]{n}=1$
83318
How to compute the limit $\lim_{n \to \infty} \sqrt[n]{a_1^n + \cdots + a_m^n}$?
50019
Prove $0$ is a partial limit of $a_n$
7105
Prove that $\prod\limits_{i=1}^n \frac{2i-1}{2i} \leq \frac{1}{\sqrt{3n+1}}$ for all $n \in \Bbb Z_+$
106281
Prove $\lim\limits_{n\to \infty}\frac{1}{\sqrt n}\left|\sum\limits_{k=1}^n (-1)^k\sqrt k\right|= \frac{1}{2}$
10451
Finding the limit of roots products $(\sqrt{2}-\sqrt[3]{2})(\sqrt{2}-\sqrt[4]{2})(\sqrt{2}-\sqrt[5]{2})\cdot \cdot \cdot (\sqrt{2}-\sqrt[n]{2})$
22347
Proving that: $\lim\limits_{n\to\infty} \left(\frac{a^{\frac{1}{n}}+b^{\frac{1}{n}}}{2}\right)^n =\sqrt{ab}$
102523
Show that $\lim\limits_{n \to \infty} \sup\limits_{k \geq n} \left(\frac{1+a_{k+1}}{a_k}\right)^k \ge e$ for any positive sequence $\{a_n\}$
29266
Limit of a sequence defined by recursive relation : $ a_n = \sqrt{a_{n-1}a_{n-2}}$
112388
Suppose $\lim \limits_{n \to ∞} a_n=L$. Prove that $\lim\limits_{n \to ∞} \frac{a_1+a_2+\cdots+a_n}{n}=L$