User Kroki

13 votes

Accepted

Coin tosses with unknown success probability

answered Aug 16, 2022 at 22:42

11 votes

Evaluate the limit $\lim\limits_{n\rightarrow \infty}\int_{0}^{\pi}\left|\sin(x)-\sin(2nx)\right|\text{ d}x$

answered Aug 10, 2022 at 19:32

11 votes

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Prove that $\sum_{a\in A} φ(a)=0$ where $A$ is finite Abelian group.

answered Apr 17, 2018 at 1:04

8 votes

Price of Option in Betting Game

answered Jul 26 at 3:32

7 votes

Finding $\displaystyle \lim_{n \rightarrow \infty} \sqrt{n} \int_0^1 \left(\frac{\sin t}{t}\right)^n dt$

answered May 15 at 3:42

6 votes

Accepted

Prove $\sum_{n=0}^\infty(-1)^n \frac{\Gamma\left(\frac{n+2}{2}\right)}{\Gamma\left(\frac{n+3}{2}\right)}=\frac{1}{\sqrt{\pi}}(\pi-2)$

answered Jun 12 at 22:35

6 votes

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What is the relation between Zeta Function and nth Integral?

answered Jul 24 at 19:16

6 votes

Idea to show $\max\left\{\int_{0}^{1}\sqrt{1+n^2x^{2n-2}} \right\}dx < 2$

answered Aug 12, 2017 at 11:22

5 votes

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Is there a sequence $(t_n)_{n\ge 0}$ such that $\lim_n t_n = \infty$, $\lim_n \Delta_n = 0$ and $\sup_n S_n < \infty$?

answered Jun 13 at 5:18

5 votes

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How to prove $\sum_{k=p}^n (-1)^k\binom{n}{k}\binom{k}{p} = (-1)^p$ by using generating functions

answered Jun 11 at 19:05

5 votes

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If $\sum a_n b_n$ converges, does $\sum \overline{a_n} b_n$ converge too?

answered May 5 at 1:38

5 votes

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$A+B+\frac{1}{2}BA^{-1}B$ is positive definite.

answered Mar 28 at 12:27

5 votes

Is convergence of vectors equivalent to convergence of inner products

answered Jun 27 at 17:53

5 votes

Accepted

Find the maximum of $\frac{\sum_{i=1}^n \sin \alpha_i}{\sum_{i=1}^n \cos \alpha_i}$ for $\sum\limits_{i=1}^n \sin^2 \alpha_i=1$

answered Jun 28 at 20:39

5 votes

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Using connectedness to prove surjectivity...

answered Sep 21, 2021 at 19:14

5 votes

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Evaluate $\lim\limits_{n\to\infty}{\dfrac{1}{n}\sum_{k=1}^n\sin{\left(\dfrac{n}{k}\right)}}$.

answered Jul 29, 2022 at 16:11

4 votes

Expectation of $f(X)$, where $X$ is normally distributed and f is the PDF of the normal distribution

answered Jun 21 at 19:31

4 votes

Box-constrained QCQP

answered Jul 23 at 14:32

4 votes

Accepted

Path dependence of $\lim\limits_{(n,m)\to(\infty, \infty)}\left(\sum_{i=1}^n \frac{1}{2^i}\right)^m$

answered May 8 at 20:27

4 votes

Reference for inequality on Frobenius/Hilbert-Schmidt matrix norm

answered May 12 at 0:27

4 votes

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Proving $\int_0^\infty t e^{2t} e^{-e^{-2t}} \mathrm{d}t = \frac{-\gamma}{4}$.

answered Aug 2 at 19:45

4 votes

Accepted

Is $f'-f$ darboux?

answered Aug 4 at 17:33

4 votes

Accepted

Show that $K(t) = \int_0^t \mathrm{e}^{-Cs} \, D \, \mathrm{e}^{-C^\intercal s} \,\mathrm{d} s$ satisfies a given equation involving $K(\infty)$

answered Aug 4 at 17:51

4 votes

Accepted

Minimum of a function defined by a sum

answered Jul 24, 2022 at 20:59

4 votes

Accepted

Probability for sum of $n$ uniform $(0, 1)$ being larger than sum of $n+1$ uniform $(0,1)$

answered Jul 26, 2022 at 6:16

4 votes

Problem on rank of a matrix-Mathematics Competition

answered Sep 20, 2021 at 15:23

4 votes

Find the sum of the value $\left|\sum_{j=1}^{\frac{p-1}{2}}w^{j^2}\right|$

answered Apr 8, 2018 at 6:28

4 votes

$g(x-y) = g(x)g(y) +f(x)f(y), f(0)= 0$

answered Aug 3, 2017 at 13:06

4 votes

Accepted

Induction proof for Tchebyshev polynomials

answered Aug 4, 2017 at 15:57

4 votes

Accepted

Basic properties of the matrix logarithm

answered Apr 5, 2018 at 21:32

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408 Answers

Coin tosses with unknown success probability

Evaluate the limit $\lim\limits_{n\rightarrow \infty}\int_{0}^{\pi}\left|\sin(x)-\sin(2nx)\right|\text{ d}x$

Prove that $\sum_{a\in A} φ(a)=0$ where $A$ is finite Abelian group.

Price of Option in Betting Game

Finding $\displaystyle \lim_{n \rightarrow \infty} \sqrt{n} \int_0^1 \left(\frac{\sin t}{t}\right)^n dt$

Prove $\sum_{n=0}^\infty(-1)^n \frac{\Gamma\left(\frac{n+2}{2}\right)}{\Gamma\left(\frac{n+3}{2}\right)}=\frac{1}{\sqrt{\pi}}(\pi-2)$

What is the relation between Zeta Function and nth Integral?

Idea to show $\max\left\{\int_{0}^{1}\sqrt{1+n^2x^{2n-2}} \right\}dx < 2$

Is there a sequence $(t_n)_{n\ge 0}$ such that $\lim_n t_n = \infty$, $\lim_n \Delta_n = 0$ and $\sup_n S_n < \infty$?

How to prove $\sum_{k=p}^n (-1)^k\binom{n}{k}\binom{k}{p} = (-1)^p$ by using generating functions

If $\sum a_n b_n$ converges, does $\sum \overline{a_n} b_n$ converge too?

$A+B+\frac{1}{2}BA^{-1}B$ is positive definite.

Is convergence of vectors equivalent to convergence of inner products

Find the maximum of $\frac{\sum_{i=1}^n \sin \alpha_i}{\sum_{i=1}^n \cos \alpha_i}$ for $\sum\limits_{i=1}^n \sin^2 \alpha_i=1$

Using connectedness to prove surjectivity...

Evaluate $\lim\limits_{n\to\infty}{\dfrac{1}{n}\sum_{k=1}^n\sin{\left(\dfrac{n}{k}\right)}}$.

Expectation of $f(X)$, where $X$ is normally distributed and f is the PDF of the normal distribution

Box-constrained QCQP

Path dependence of $\lim\limits_{(n,m)\to(\infty, \infty)}\left(\sum_{i=1}^n \frac{1}{2^i}\right)^m$

Reference for inequality on Frobenius/Hilbert-Schmidt matrix norm

Proving $\int_0^\infty t e^{2t} e^{-e^{-2t}} \mathrm{d}t = \frac{-\gamma}{4}$.

Is $f'-f$ darboux?

Show that $K(t) = \int_0^t \mathrm{e}^{-Cs} \, D \, \mathrm{e}^{-C^\intercal s} \,\mathrm{d} s$ satisfies a given equation involving $K(\infty)$

Minimum of a function defined by a sum

Probability for sum of $n$ uniform $(0, 1)$ being larger than sum of $n+1$ uniform $(0,1)$

Problem on rank of a matrix-Mathematics Competition

Find the sum of the value $\left|\sum_{j=1}^{\frac{p-1}{2}}w^{j^2}\right|$

$g(x-y) = g(x)g(y) +f(x)f(y), f(0)= 0$

Induction proof for Tchebyshev polynomials

Basic properties of the matrix logarithm