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537 Questions

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934

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Sum of series $\sum \limits_{k=1}^{\infty}\frac{\sin^3 3^k}{3^k}$

sequences-and-series

Aug 5 '17 at 22:01 Khosrotash 16.7k

votes

answers

views

Number which is simultaneously sum of 2 and 3 squares [closed]

number-theory

Nov 26 '17 at 3:16 Rivasa 664

votes

answers

views

Solve an equation of 4th degree

algebra-precalculus

Apr 19 '16 at 21:14 stackErr 228

votes

answers

views

Infinite group has infinitely many subgroups, namely cyclic subgroups.

abstract-algebra group-theory proof-verification

Dec 1 '17 at 1:02 lhf 168k

votes

answers

171

views

Problem 30 from Shakarchi Stein's book

real-analysis measure-theory

Oct 1 at 6:25 Sangchul Lee 96.8k

votes

answer

637

views

Definition of isomorphism from Herstein's book

abstract-algebra group-theory definition

Dec 23 '17 at 17:54 egreg 186k

votes

answer

views

Every separable metric space has a countable base

general-topology proof-verification metric-spaces

Jun 4 '16 at 9:47 ZFR 5,359

votes

answers

views

A finite set is closed

real-analysis metric-spaces

Jun 8 '15 at 22:26 aexl 1,287

votes

answers

views

Ternary representation of Cantor set

real-analysis cantor-set

Feb 11 at 4:55 Kumar Nilesh 11

votes

answers

126

views

Solve the equation $\sqrt{1-x}=2x^2-1+2x\sqrt{1-x^2}$

algebra-precalculus

Sep 24 at 14:23 астон вілла олоф мэллбэрг 40.7k

votes

answers

131

views

Coloring of $\mathbb{R}^3$ into 3 colors

combinatorics proof-verification contest-math

Nov 18 '17 at 20:21 Michael Seifert 5,192

votes

answers

743

views

Problem 15 from Herstein's book

functions elementary-set-theory

Nov 10 '17 at 0:27 gt6989b 36k

votes

answers

222

views

Proof $\int \limits_{0}^{\infty}\left(\frac{\sin x}{x}\right)^2dx=\frac{\pi}{2}$ by definition

real-analysis

Dec 11 '16 at 15:23 SomeStrangeUser 1,665

votes

answers

887

views

The equivalence of definitions Riemann integral

real-analysis riemann-integration

Jun 18 '16 at 10:22 Community♦ 1

votes

answer

171

views

$\int \limits_{E}|f|d\mu<\varepsilon$ whenever $\mu(E)<\delta$.

real-analysis measure-theory proof-verification

Jun 14 '16 at 6:12 ZFR 5,359

votes

answer

600

views

Dirichlet series

real-analysis sequences-and-series convergence

May 18 '14 at 12:28 Daniel Fischer 174k

votes

answers

195

views

“up to associates” in the Euclidean domain

abstract-algebra gaussian-integers

Aug 27 at 17:23 egreg 186k

votes

answers

203

views

Monotone Convergence theorem for decreasing sequence

real-analysis measure-theory proof-verification monotone-functions

Aug 18 at 14:53 Mayuresh L 1,331

votes

answers

views

Evaluate $\sum\limits_{n=1}^{2016}\frac{1}{n!+(n+1)!+(n+2)!}$

sequences-and-series

Jan 22 '18 at 8:33 ZFR 5,359

votes

answers

960

views

Identity of Fibonacci sequence

fibonacci-numbers

Nov 28 '17 at 15:03 ZFR 5,359

votes

answers

468

views

Compute the integral $\int \limits_{0}^{\pi}\frac{\sin 100x}{\sin x}dx$ [closed]

integration

Oct 30 '17 at 10:06 Guy Fsone 17.3k

votes

answers

130

views

Lagrange multiplier to function $x^2+y^2+z^2$

lagrange-multiplier

Oct 17 '17 at 7:15 mfl 26.9k

votes

answers

views

Find the limit of $6^n(2-x_n)$ where $x_n=\sqrt[3]{6+\sqrt[3]{6+\dots+\sqrt[3]{6}}}$ with $n$ roots

sequences-and-series

Sep 7 '17 at 8:00 Guy Fsone 17.3k

votes

answer

129

views

Theorem 2.22 from RCA Rudin

real-analysis measure-theory

Jul 2 '16 at 7:09 Eric Wofsey 193k

votes

answers

908

views

Definition of positive measure

real-analysis measure-theory

May 22 '16 at 14:41 Hurkyl 112k

votes

answers

341

views

Riemann integral of continuous non-negative function

real-analysis

Nov 6 '15 at 12:35 Math1000 19.4k

votes

answer

207

views

Problem 19 chapter 4 from baby Rudin

real-analysis

Sep 28 '15 at 22:33 Community♦ 1

votes

answer

views

Compact set of real numbers with countably many limit points.

real-analysis general-topology compactness

Jul 7 '15 at 20:40 mathcounterexamples.net 26.9k

votes

answer

views

Non Noetherian ring with only one prime ideal

ring-theory commutative-algebra

Jan 30 at 13:43 ZFR 5,359

votes

answers

109

views

The notion of limsup for sets

real-analysis measure-theory elementary-set-theory limsup-and-liminf

Sep 17 at 8:56 X.X 35

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537 Questions

Sum of series $\sum \limits_{k=1}^{\infty}\frac{\sin^3 3^k}{3^k}$

Number which is simultaneously sum of 2 and 3 squares [closed]

Solve an equation of 4th degree

Infinite group has infinitely many subgroups, namely cyclic subgroups.

Problem 30 from Shakarchi Stein's book

Definition of isomorphism from Herstein's book

Every separable metric space has a countable base

A finite set is closed

Ternary representation of Cantor set

Solve the equation $\sqrt{1-x}=2x^2-1+2x\sqrt{1-x^2}$

Coloring of $\mathbb{R}^3$ into 3 colors

Problem 15 from Herstein's book

Proof $\int \limits_{0}^{\infty}\left(\frac{\sin x}{x}\right)^2dx=\frac{\pi}{2}$ by definition

The equivalence of definitions Riemann integral

$\int \limits_{E}|f|d\mu<\varepsilon$ whenever $\mu(E)<\delta$.

Dirichlet series

“up to associates” in the Euclidean domain

Monotone Convergence theorem for decreasing sequence

Evaluate $\sum\limits_{n=1}^{2016}\frac{1}{n!+(n+1)!+(n+2)!}$

Identity of Fibonacci sequence

Compute the integral $\int \limits_{0}^{\pi}\frac{\sin 100x}{\sin x}dx$ [closed]

Lagrange multiplier to function $x^2+y^2+z^2$

Find the limit of $6^n(2-x_n)$ where $x_n=\sqrt[3]{6+\sqrt[3]{6+\dots+\sqrt[3]{6}}}$ with $n$ roots

Theorem 2.22 from RCA Rudin

Definition of positive measure

Riemann integral of continuous non-negative function

Problem 19 chapter 4 from baby Rudin

Compact set of real numbers with countably many limit points.

Non Noetherian ring with only one prime ideal

The notion of limsup for sets