Question

How to get the identity $\frac{1}{ab} = \left(\frac{1}{a} - \frac{1}{b}\right)\frac{1}{(b - a)}$ when $a < b$?

score 66 · Answer 1 · 2026-04-14 13:17:38

66

Views

How to get the identity $\frac{1}{ab} = \left(\frac{1}{a} - \frac{1}{b}\right)\frac{1}{(b - a)}$ when $a < b$?

Published on 14 Apr 2026 - 13:17

score 439 · Answer 2 · 2026-04-17 14:40:49

439

Views

Proving the answer to the integral of $\sin(π/x^2)$

Published on 17 Apr 2026 - 14:40

score 67 · Answer 3 · 2026-04-17 13:15:48

67

Views

How to write this $(\exists (x,y) \in R, y- 3x-2 \wedge y = 1-x^2) $in words?

Published on 17 Apr 2026 - 13:15

score 1.1k · Answer 4 · 2026-04-15 07:45:57

1.1k

Views

Conjugate symmetry of an inner product

Published on 15 Apr 2026 - 7:45

score 94 · Answer 5 · 2026-04-14 16:46:08

94

Views

What is the correct way to prove that for all $m \in Z$, if $m$ is even then then $mn$ is even?

Published on 14 Apr 2026 - 16:46

score 92 · Answer 6 · 2026-04-14 23:32:26

92

Views

Is this correct approach to proving $xy=0$?

Published on 14 Apr 2026 - 23:32

score 60 · Answer 7 · 2026-04-15 00:59:55

60

Views

King of the hill game

Published on 15 Apr 2026 - 0:59

score 1.4k · Answer 8 · 2026-04-13 16:57:15

1.4k

Views

Prove that $\frac{k^7}{7}+\frac{k^5}{5}+\frac{2k^3}{3}-\frac{k}{105}$ is an integer.

Published on 13 Apr 2026 - 16:57

score 102 · Answer 9 · 2026-04-16 20:07:29

102

Views

$gcd(m,n) = gcd(a\cdot m+b\cdot n,c\cdot m+d\cdot n)$

Published on 16 Apr 2026 - 20:07

score 53 · Answer 10 · 2026-04-12 20:53:05

53

Views

If $a\mid b$, then $\forall x(b\in \mathbb z) \exists y(a \in \mathbb Z/a\mathbb Z([x]b\subseteq [y]a.$

Published on 12 Apr 2026 - 20:53

score 38 · Answer 11 · 2026-04-15 20:14:38

38

Views

An example $\limsup \mu_n(F)<\mu(F)$

Published on 15 Apr 2026 - 20:14

score 114 · Answer 12 · 2026-04-16 12:53:05

114

Views

How to show $x_1y_1 + x_2y_2 - (x_3y_3 + x_4y_4) > 0$

Published on 16 Apr 2026 - 12:53

score 576 · Answer 13 · 2026-04-16 06:06:40

576

Views

If $x$ and $y$ are arbitrary real numbers with $x < y$, prove that there exists at least one real satisfying $x < z < y$

Published on 16 Apr 2026 - 6:06

score 60 · Answer 14 · 2026-04-09 19:09:18

60

Views

Logical mistake in a proof of Dirichlet's test

Published on 09 Apr 2026 - 19:09

score 68 · Answer 15 · 2026-04-16 14:03:53

68

Views

Proof that $\int_{0}^{1}\frac{1}{x-\ln(x)}\mathbb{d}x$ is convergent.

Published on 16 Apr 2026 - 14:03

List Question

How to get the identity $\frac{1}{ab} = \left(\frac{1}{a} - \frac{1}{b}\right)\frac{1}{(b - a)}$ when $a < b$?

Proving the answer to the integral of $\sin(π/x^2)$

How to write this $(\exists (x,y) \in R, y- 3x-2 \wedge y = 1-x^2) $in words?

Conjugate symmetry of an inner product

What is the correct way to prove that for all $m \in Z$, if $m$ is even then then $mn$ is even?

Is this correct approach to proving $xy=0$?

King of the hill game

Prove that $\frac{k^7}{7}+\frac{k^5}{5}+\frac{2k^3}{3}-\frac{k}{105}$ is an integer.

$gcd(m,n) = gcd(a\cdot m+b\cdot n,c\cdot m+d\cdot n)$

If $a\mid b$, then $\forall x(b\in \mathbb z) \exists y(a \in \mathbb Z/a\mathbb Z([x]b\subseteq [y]a.$

An example $\limsup \mu_n(F)<\mu(F)$

How to show $x_1y_1 + x_2y_2 - (x_3y_3 + x_4y_4) > 0$

If $x$ and $y$ are arbitrary real numbers with $x < y$, prove that there exists at least one real satisfying $x < z < y$

Logical mistake in a proof of Dirichlet's test

Proof that $\int_{0}^{1}\frac{1}{x-\ln(x)}\mathbb{d}x$ is convergent.

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