Question

$\left\lfloor \frac{1}{\sqrt{1}}+\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}+\frac{1}{\sqrt{4}}+...+\frac{1}{\sqrt{1024}}\right\rfloor =?$

score 946 · Answer 1 · 2017-11-16 11:04:47

946

Views

$\left\lfloor \frac{1}{\sqrt{1}}+\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}+\frac{1}{\sqrt{4}}+...+\frac{1}{\sqrt{1024}}\right\rfloor =?$

Published on 16 Nov 2017 - 11:04

score 834 · Answer 2 · 2017-11-16 12:50:44

834

Views

Show that the only matrices commuting with idempotent matrices are scalar matrices

Published on 16 Nov 2017 - 12:50

score 440 · Answer 3 · 2026-04-10 04:45:51

440

Views

Functions such that $f(ax)=f(x)+f(a)$

Published on 10 Apr 2026 - 4:45

score 1.3k · Answer 4 · 2017-11-17 07:48:13

1.3k

Views

Finding dimension of the vector spaces of polynomials with two commuting variables as well as two non-commuting variables

Published on 17 Nov 2017 - 7:48

score 1.7k · Answer 5 · 2017-11-19 04:36:15

1.7k

Views

Prove rigorously that $\inf\{\frac{1}{n}: n \in \mathbb{N} \}=0$

Published on 19 Nov 2017 - 4:36

score 87 · Answer 6 · 2017-11-19 19:38:44

87

Views

Solving $a + b + c = 57, a^2 + b^2 - c^2 = z, zc = 2017$ in integers

Published on 19 Nov 2017 - 19:38

score 203 · Answer 7 · 2017-11-19 21:47:00

203

Views

$x^2+y^2=1\Rightarrow \exists\theta\in (-\pi,\pi]: x=\sin\theta, y=\cos\theta$

Published on 19 Nov 2017 - 21:47

score 553 · Answer 8 · 2026-04-12 13:50:38

553

Views

Sum of all permutations of degree $n$

Published on 12 Apr 2026 - 13:50

score 471 · Answer 9 · 2017-11-20 06:40:13

471

Views

True or false? if $p$ and $q$ divide $n$, and each is greater than $n^{1/4}$, then $n/pq$ is prime

Published on 20 Nov 2017 - 6:40

score 691 · Answer 10 · 2017-11-21 11:36:34

691

Views

Let $p(x)$ be a real $7$ degree polynomial with $p(\pi)=\sqrt 3$ and $\int_{-\pi}^{\pi}x^k p(x)=0$ for $0\le k\le 6$. Find $p(0)$ and $p(-\pi)$.

Published on 21 Nov 2017 - 11:36

score 118 · Answer 11 · 2026-04-12 00:30:42

118

Views

Digitangular numbers

Published on 12 Apr 2026 - 0:30

score 39 · Answer 12 · 2026-04-10 23:57:54

39

Views

How would you go about proving this without using its contrapositive?

Published on 10 Apr 2026 - 23:57

score 93 · Answer 13 · 2017-11-23 11:20:45

Prove that, for prime $p$, the sum of products of numbers taken $r<p-1$ at a time from the set $\{1,2,\dots,p-1\}$ is always divisible by $p$.

score 166 · Answer 14 · 2026-04-12 12:48:32

166

Views

Finding the trace of $T^4$ and $T^2$?

Published on 12 Apr 2026 - 12:48

score 144 · Answer 15 · 2017-11-24 16:32:43

144

Views

Show that $V = \{\langle x, y \rangle \ | \ x \geq 0 \ \text{and} \ y \in \mathbb{R}\}$ is closed.

Published on 24 Nov 2017 - 16:32

List Question

$\left\lfloor \frac{1}{\sqrt{1}}+\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}+\frac{1}{\sqrt{4}}+...+\frac{1}{\sqrt{1024}}\right\rfloor =?$

Show that the only matrices commuting with idempotent matrices are scalar matrices

Functions such that $f(ax)=f(x)+f(a)$

Finding dimension of the vector spaces of polynomials with two commuting variables as well as two non-commuting variables

Prove rigorously that $\inf\{\frac{1}{n}: n \in \mathbb{N} \}=0$

Solving $a + b + c = 57, a^2 + b^2 - c^2 = z, zc = 2017$ in integers

$x^2+y^2=1\Rightarrow \exists\theta\in (-\pi,\pi]: x=\sin\theta, y=\cos\theta$

Sum of all permutations of degree $n$

True or false? if $p$ and $q$ divide $n$, and each is greater than $n^{1/4}$, then $n/pq$ is prime

Let $p(x)$ be a real $7$ degree polynomial with $p(\pi)=\sqrt 3$ and $\int_{-\pi}^{\pi}x^k p(x)=0$ for $0\le k\le 6$. Find $p(0)$ and $p(-\pi)$.

Digitangular numbers

How would you go about proving this without using its contrapositive?

Prove that, for prime $p$, the sum of products of numbers taken $r<p-1$ at a time from the set $\{1,2,\dots,p-1\}$ is always divisible by $p$.

Finding the trace of $T^4$ and $T^2$?

Show that $V = \{\langle x, y \rangle \ | \ x \geq 0 \ \text{and} \ y \in \mathbb{R}\}$ is closed.

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