query: Prove that $\frac{\xi}{n} \to 0$ , where $\xi = \max(f_1 \dots f_n)$
positive_passages.docid: 24683
positive_passages.text: For i.i.d. $\{X_n\}$ proving $\frac1n\max\limits_{1\leqslant k\leqslant n}|X_k|\xrightarrow{\mathrm{a.s.}}0\Leftrightarrow E(|X_1|)<+∞$
negative_passages.docid: 132126
negative_passages.text: Proving $\sum\limits_{n=1}^{\infty } \frac{\mu (n)}n=0$ where $\mu$ is the Möbius function
negative_passages.docid: 119053
negative_passages.text: How to prove that $\displaystyle f''(a)=\lim_{h \to 0}\frac{f(a+2h)-2f(a+h)+f(a)}{h^2}$
negative_passages.docid: 89186
negative_passages.text: Showing that $\frac{X_{(i)}}{X_{(n)}},i=1,2,...,n-1$ and $X_{(n)}$ are independent for a population with df $F(y)=y^{\theta}$
negative_passages.docid: 39073
negative_passages.text: Proving that: $\forall n \in \mathbb{N} :|f^{(n)}(x)|\leq \frac{1}{n+1}$
negative_passages.docid: 57778
negative_passages.text: Convergence in Distribution of the maximum of a sequence.
negative_passages.docid: 103757
negative_passages.text: how can I prove that $\frac{\arctan x}{x }< 1$?
negative_passages.docid: 58041
negative_passages.text: Prove by Mean Value Theorem $\frac{x}{1+x}0$
negative_passages.docid: 78319
negative_passages.text: Show that $x \mapsto \frac{f(x)}{x}$ is strictly increasing on (0,1) given that f '(x) is strictly increasing on (0,1) and that f(0)=0
negative_passages.docid: 51107
negative_passages.text: Limit distribution of $\frac1n\cdot \max(X_1,X_2,...,X_n)$ for $(X_n)$ i.i.d. standard Cauchy
negative_passages.docid: 349
negative_passages.text: Prove $| \sum_{i \leq n} \frac{\mu(i)}{i} | \leq 1$
negative_passages.docid: 61731
negative_passages.text: Prove that for each $n \in \mathbb N$, $\gamma_n=1+\frac{1}{2}+\dots+\frac{1}{n}-\int_1^n \frac{1}{x}dx$ is convergent
negative_passages.docid: 33495
negative_passages.text: A limit problem about $a_{n+1}=a_n+\frac{n}{a_n}$
negative_passages.docid: 139674
negative_passages.text: Prove $\ln\frac{p}{q}\leq \frac{p-q}{\sqrt{pq}}$ for $0<q\leq p$
negative_passages.docid: 13533
negative_passages.text: Proof that the limit of $\frac{1}{x}$ as $x$ approaches $0$ does not exist
negative_passages.docid: 96127
negative_passages.text: Maximum of $|\sin(z)|$ as $\{z: |z| \leq 1 \} $
negative_passages.docid: 145496
negative_passages.text: Show $\lim_{h \to \ 0} \frac{f(x + 2h) - 2f(x+h) + f(x)}{h^{2}} = f''(x)$ Proof verification