User r9m

43 votes

1 answer

1k views

Stronger version of AMM problem 11145 (April 2005)?

asked Jul 1, 2014 at 15:25

39 votes

1 answer

1k views

Evaluating the limit: $\lim\limits_{x \to \infty} \sum\limits_{n=1}^{\infty} (-1)^{n-1}\frac{x^{2n-1}}{(2n)! \log (2n)}$

asked Feb 13, 2017 at 23:40

29 votes

1 answer

2k views

Finding the limit of a sequence with an undesirable $\ln k$

asked Jun 10, 2014 at 1:13

25 votes

3 answers

1k views

Is every natural number representable as $\sum\limits_{k=1}^{n} \pm k^3$?

asked Dec 23, 2014 at 11:24

21 votes

3 answers

2k views

Sum of Harmonic numbers $\sum\limits_{n=1}^{\infty} \frac{H_n^{(2)}}{2^nn^2}$

asked Nov 15, 2014 at 16:07

21 votes

4 answers

1k views

A problem with concyclic points on $\mathbb{R}^2$

asked Mar 4, 2014 at 3:44

19 votes

4 answers

467 views

Integrating $\int_0^{\pi/2} \frac{\sin^2 ax}{\sin^2 x}\,dx$

asked Mar 16, 2016 at 7:30

15 votes

1 answer

776 views

Closed form of $\int_0^{\pi/2} \frac{\arctan^2 (\sin^2 \theta)}{\sin^2 \theta}\,d\theta$

asked Apr 13, 2016 at 17:48

12 votes

1 answer

265 views

Points of differentiability of $f(x) = \sum\limits_{n : q_n < x} c_n$

asked Sep 10, 2016 at 1:59

10 votes

3 answers

314 views

An Inequality Problem $1 \le \frac{a}{1-ab}+\frac{b}{1-bc}+\frac{c}{1-ac} \le \frac{3\sqrt{3}}{2}$

asked May 31, 2014 at 1:09

10 votes

0 answers

151 views

An Inequality with complex numbers and $1/\pi$ [duplicate]

asked Nov 4, 2014 at 18:12

10 votes

1 answer

450 views

Bounds on derivative of real positive coefficient polynomial satisfying certain properties

asked Nov 11, 2014 at 5:33

9 votes

1 answer

300 views

Prove that for $n$ and $m$ integers: $ 3^mn \mid \sum\limits_{k=0}^{m} {\binom{3m}{3k}}(3n-1)^k$

asked Jun 6, 2014 at 2:08

9 votes

1 answer

147 views

A problem about oriented face in Square grid

asked Aug 28, 2016 at 10:08

9 votes

1 answer

702 views

An Inequality for sides and diagonal of convex quadrilateral from AMM

asked Oct 5, 2015 at 20:20

8 votes

1 answer

408 views

Combinatorial Interpretation of a Binomial Identity

asked Nov 28, 2014 at 17:00

8 votes

3 answers

248 views

An Inequality Problem with not nice conditions

asked Apr 13, 2014 at 16:58

7 votes

1 answer

246 views

Determining the best possible constant $k$, for an Integral Inequality

asked Jul 13, 2014 at 12:32

7 votes

1 answer

168 views

Constructing a function with constant line integral in $\mathbb{R}^n$?

asked Aug 27, 2018 at 19:24

7 votes

1 answer

2k views

Condition for Self-Adjoint Sturm-Liouville Operator

asked Dec 27, 2016 at 20:31

5 votes

1 answer

425 views

Convergence in probability from Cesaro mean

asked Nov 7, 2017 at 16:08

5 votes

0 answers

336 views

A problem with sign of coefficients of a polynomial expression

asked Jun 22, 2014 at 18:03

5 votes

1 answer

194 views

Problem with a sequence with multiple integrals [duplicate]

asked Apr 18, 2014 at 13:40

4 votes

2 answers

3k views

Existence of Saddle Point of a Matrix (Shapley's Theorem)

asked Feb 17, 2014 at 19:18

4 votes

1 answer

138 views

Determining the asymptotics of the Summatory function of an Arithmetic Function

asked Nov 20, 2014 at 20:26

3 votes

1 answer

224 views

Limit of the sequence $ x_{n+1}=x_n+\sqrt{a+x_n^2}$

asked Jun 25, 2014 at 1:27

2 votes

1 answer

125 views

Satisfying Functional Equations

asked Feb 15, 2014 at 17:23

2 votes

1 answer

135 views

Solution to a Functional Equation $g'(x)=\dfrac{g(bx)-g(x)}{(b-1)x}$

asked Mar 20, 2014 at 7:49

2 votes

1 answer

91 views

A problem with moments of a function

asked Apr 8, 2014 at 10:07

2 votes

1 answer

157 views

A Problem with Intermediate Value Property and a partial converse question

asked May 6, 2014 at 2:46

Stack Exchange Network

31 Questions

Stronger version of AMM problem 11145 (April 2005)?

Evaluating the limit: $\lim\limits_{x \to \infty} \sum\limits_{n=1}^{\infty} (-1)^{n-1}\frac{x^{2n-1}}{(2n)! \log (2n)}$

Finding the limit of a sequence with an undesirable $\ln k$

Is every natural number representable as $\sum\limits_{k=1}^{n} \pm k^3$?

Sum of Harmonic numbers $\sum\limits_{n=1}^{\infty} \frac{H_n^{(2)}}{2^nn^2}$

A problem with concyclic points on $\mathbb{R}^2$

Integrating $\int_0^{\pi/2} \frac{\sin^2 ax}{\sin^2 x}\,dx$

Closed form of $\int_0^{\pi/2} \frac{\arctan^2 (\sin^2 \theta)}{\sin^2 \theta}\,d\theta$

Points of differentiability of $f(x) = \sum\limits_{n : q_n < x} c_n$

An Inequality Problem $1 \le \frac{a}{1-ab}+\frac{b}{1-bc}+\frac{c}{1-ac} \le \frac{3\sqrt{3}}{2}$

An Inequality with complex numbers and $1/\pi$ [duplicate]

Bounds on derivative of real positive coefficient polynomial satisfying certain properties

Prove that for $n$ and $m$ integers: $ 3^mn \mid \sum\limits_{k=0}^{m} {\binom{3m}{3k}}(3n-1)^k$

A problem about oriented face in Square grid

An Inequality for sides and diagonal of convex quadrilateral from AMM

Combinatorial Interpretation of a Binomial Identity

An Inequality Problem with not nice conditions

Determining the best possible constant $k$, for an Integral Inequality

Constructing a function with constant line integral in $\mathbb{R}^n$?

Condition for Self-Adjoint Sturm-Liouville Operator

Convergence in probability from Cesaro mean

A problem with sign of coefficients of a polynomial expression

Problem with a sequence with multiple integrals [duplicate]

Existence of Saddle Point of a Matrix (Shapley's Theorem)

Determining the asymptotics of the Summatory function of an Arithmetic Function

Limit of the sequence $ x_{n+1}=x_n+\sqrt{a+x_n^2}$

Satisfying Functional Equations

Solution to a Functional Equation $g'(x)=\dfrac{g(bx)-g(x)}{(b-1)x}$

A problem with moments of a function

A Problem with Intermediate Value Property and a partial converse question