Question

Proving convergence of a sequence $(y_n)$ under certain conditions.

score 58 · Answer 1 · 2026-04-16 05:46:04

58

Views

Proving convergence of a sequence $(y_n)$ under certain conditions.

Published on 16 Apr 2026 - 5:46

score 473 · Answer 2 · 2026-04-17 11:40:40

473

Views

Let $f:A \rightarrow B$ be a bijective map, and let $P,Q \subseteq A$ be any sets. Then $f(P-Q)=f(P)-f(Q)$

Published on 17 Apr 2026 - 11:40

score 105 · Answer 3 · 2026-04-13 21:35:58

105

Views

Finding Area depending upon following condition

Published on 13 Apr 2026 - 21:35

score 822 · Answer 4 · 2026-04-15 03:50:42

822

Views

When is the Lagrange interpolation polynomial exact?

Published on 15 Apr 2026 - 3:50

score 923 · Answer 5 · 2026-04-17 01:03:44

923

Views

If $f:\mathbb{R}\setminus\{0,1\}\to\mathbb{R}$ satisfies $f(x)+2f\left(\frac 1 x\right)+3f\left(\frac x {x-1}\right)=x$, then $8f(4)=?$

Published on 17 Apr 2026 - 1:03

score 128 · Answer 6 · 2026-04-18 13:46:09

128

Views

Prove that $B\cup(\bigcap \mathcal F)=\bigcap_{A\in \mathcal F}(B\cup A)$.

Published on 18 Apr 2026 - 13:46

score 49 · Answer 7 · 2026-04-17 00:31:13

49

Views

Prove that $[G: S]=[\phi [G]: \phi [S]] \cdot[N: S \cap N]$

Published on 17 Apr 2026 - 0:31

score 76 · Answer 8 · 2026-04-14 10:47:29

76

Views

Infer the second isomorphism theorem from the first one

Published on 14 Apr 2026 - 10:47

score 203 · Answer 9 · 2026-04-16 05:33:41

203

Views

Prove that $a$ commutes with each of its conjugates in $G$ if and only if $a$ belongs to an abelian normal subgroup of $G$.

Published on 16 Apr 2026 - 5:33

score 100 · Answer 10 · 2026-04-15 06:25:56

100

Views

Proof verification that $t(n+1)=t(n) + \pi$ using mathematical induction

Published on 15 Apr 2026 - 6:25

score 749 · Answer 11 · 2026-04-17 10:19:43

749

Views

Prove that $\tan^{-1}\frac{\sqrt{1+x^2}+\sqrt{1-x^2}}{\sqrt{1+x^2}-\sqrt{1-x^2}}=\frac{\pi}{4}+\frac 12 \cos^{-1}x^2$

Published on 17 Apr 2026 - 10:19

score 47 · Answer 12 · 2026-04-17 15:17:44

47

Views

Solution verification: Harmonic polynomial $p \in \mathbb{R}[x_1, \dots, x_n]$ divisible by $x_1^2+\dots+x_n^2$ must be identically $0.$

Published on 17 Apr 2026 - 15:17

score 153 · Answer 13 · 2026-04-11 01:05:03

153

Views

Proof that homotopy is a transitive property.

Published on 11 Apr 2026 - 1:05

score 255 · Answer 14 · 2026-04-17 08:37:34

255

Views

If collection of subgroups of $G$ form a chain , then $G$ is cyclic?

Published on 17 Apr 2026 - 8:37

score 615 · Answer 15 · 2026-04-16 16:04:22

615

Views

Prove that for every integer $x$, if $x$ is odd then there exists an integer $y$ such that $x^2=4y+1$.

Published on 16 Apr 2026 - 16:04

List Question

Proving convergence of a sequence $(y_n)$ under certain conditions.

Let $f:A \rightarrow B$ be a bijective map, and let $P,Q \subseteq A$ be any sets. Then $f(P-Q)=f(P)-f(Q)$

Finding Area depending upon following condition

When is the Lagrange interpolation polynomial exact?

If $f:\mathbb{R}\setminus\{0,1\}\to\mathbb{R}$ satisfies $f(x)+2f\left(\frac 1 x\right)+3f\left(\frac x {x-1}\right)=x$, then $8f(4)=?$

Prove that $B\cup(\bigcap \mathcal F)=\bigcap_{A\in \mathcal F}(B\cup A)$.

Prove that $[G: S]=[\phi [G]: \phi [S]] \cdot[N: S \cap N]$

Infer the second isomorphism theorem from the first one

Prove that $a$ commutes with each of its conjugates in $G$ if and only if $a$ belongs to an abelian normal subgroup of $G$.

Proof verification that $t(n+1)=t(n) + \pi$ using mathematical induction

Prove that $\tan^{-1}\frac{\sqrt{1+x^2}+\sqrt{1-x^2}}{\sqrt{1+x^2}-\sqrt{1-x^2}}=\frac{\pi}{4}+\frac 12 \cos^{-1}x^2$

Solution verification: Harmonic polynomial $p \in \mathbb{R}[x_1, \dots, x_n]$ divisible by $x_1^2+\dots+x_n^2$ must be identically $0.$

Proof that homotopy is a transitive property.

If collection of subgroups of $G$ form a chain , then $G$ is cyclic?

Prove that for every integer $x$, if $x$ is odd then there exists an integer $y$ such that $x^2=4y+1$.

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