query: Proving $\left\| \frac{\vec{v}}{\|\vec{v}\|}\right\| =1$, $\vec{v}\ne \vec{0}$
positive_passages.docid: 156985
positive_passages.text: Question Concerning Vectors
negative_passages.docid: 71547
negative_passages.text: Prove $ 1+\left( 1-\frac{x}{n}\right)+...+\left(1-\frac{x}{n}\right)^{n-1}=\frac{n}{x}\left(1-\left(1-\frac{x}{n}\right)^n\right)$
negative_passages.docid: 138683
negative_passages.text: Proving $\prod_{i=2}^{i=n} \left(1-\frac{1}{i^2}\right) = \frac{n+1}{2n}$ by induction
negative_passages.docid: 13899
negative_passages.text: Proof that $-v = (-1)*v$
negative_passages.docid: 49109
negative_passages.text: Proving $\gcd \left(\frac{a}{\gcd (a,b)},\frac{b}{\gcd (a,b)}\right)=1$
negative_passages.docid: 76110
negative_passages.text: Proving that the zero vector is unique
negative_passages.docid: 62065
negative_passages.text: Prove that $v_1, \dots v_n$ is a basis of V.
negative_passages.docid: 95379
negative_passages.text: Prove that $V = V_1 \oplus V_2$ in the following
negative_passages.docid: 105145
negative_passages.text: Show that $\mathbb{E}\left(\bar{X}_{n}\mid X_{(1)},X_{(n)}\right) = \frac{X_{(1)}+X_{(n)}}{2}$
negative_passages.docid: 67820
negative_passages.text: Showing that $(A_{ij})=\left(\frac1{1+x_i+x_j}\right)$ is positive semidefinite
negative_passages.docid: 49806
negative_passages.text: Prove that $\frac{R/ \ker \phi}{(\ker \phi + J)/ \ker \phi} \cong \frac{S}{\phi(J)}$
negative_passages.docid: 145423
negative_passages.text: prove that if $1 \le m \le n$ then $\left(1+\frac1n\right)^m < 1+\frac mn + \left(\frac mn\right)^2$
negative_passages.docid: 73191
negative_passages.text: Proving that $\frac{1}{1\cdot 2} + \frac{1}{2\cdot 3} + \frac{1}{3 \cdot 4} +\ldots + \frac{1}{n(n+1)} = \frac{n}{n+1}$
negative_passages.docid: 49296
negative_passages.text: Prove $|(1+|u|^2)v-(1+|v|^2)u|>|u\bar{v}-\bar{u}v|$
negative_passages.docid: 349
negative_passages.text: Prove $| \sum_{i \leq n} \frac{\mu(i)}{i} | \leq 1$
negative_passages.docid: 35611
negative_passages.text: How can I show that $n! \leqslant \left(\frac{n+1}{2}\right)^n$?
negative_passages.docid: 104807
negative_passages.text: Prove the inequality $\left|\frac{m}{n}-\frac{1+\sqrt{5}}{2}\right|<\frac{1}{mn}$