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Kroki's user avatar
Kroki's user avatar
Kroki
  • Member for 6 years, 11 months
  • Last seen this week
  • Montreal, QC, Canada
13 votes
Accepted

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

13 votes
Accepted

Coin tosses with unknown success probability

11 votes

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

8 votes

Price of Option in Betting Game

7 votes
Accepted

Is it always true that if $x_n\to0$, $y_n\to0$ there exist $\epsilon_n\in\{-1,1\}$ such that both $\sum\epsilon_nx_n$and $\sum\epsilon_ny_n$ converge?

7 votes

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

6 votes
Accepted

Examples which show $\|\cdot\|_p$ on $L^p$ is not induced by an inner product (Parallelogram law)

6 votes

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

6 votes
Accepted

Possibility of bounding $\sum_{n=0}^N |a_n|$ from above by $\sup_{z\in (0,1)} |\sum_{1\leq n\leq N} (1+z+\ldots+z^{n-1}) a_n|$

6 votes

Proof of expected length in random division of $[0,1]$ interval

6 votes
Accepted

Prove that $\mathbb{E}\exp{\lambda\xi} \le \exp\left(\lambda^2 \Vert\xi\Vert_{\psi_2}^2\right)$

6 votes
Accepted

What is the relation between Zeta Function and nth Integral?

6 votes
Accepted

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

5 votes
Accepted

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

5 votes
Accepted

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

5 votes
Accepted

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

5 votes

Is convergence of vectors equivalent to convergence of inner products

5 votes
Accepted

Evaluating $\lim_{n\to \infty} n \int_{0}^{1} \frac{x^n}{x+1} dx$

5 votes

Does $\int_{-\infty}^{\infty}\ln\left(e^{-x^{2}}+1\right)dx=\frac{3\pi}{4}-1$?

5 votes

Show that $ \Vert Tx_\varepsilon -x_\varepsilon \Vert \leq \varepsilon $

5 votes
Accepted

Basic properties of the matrix logarithm

5 votes
Accepted

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

5 votes
Accepted

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

5 votes
Accepted

Using connectedness to prove surjectivity...

5 votes
Accepted

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

4 votes
Accepted

Minimum of a function defined by a sum

4 votes
Accepted

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

4 votes

Problem on rank of a matrix-Mathematics Competition

4 votes

An inequality on trace of product of two matrices

4 votes

Reference for inequality on Frobenius/Hilbert-Schmidt matrix norm

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