User adfriedman

12 votes

Probability of getting a second $6$

answered May 2, 2017 at 10:21

10 votes

Accepted

Questions on proof of theorem 2.30 in Baby Rudin.

answered Feb 23, 2017 at 4:27

9 votes

Calculate $∑_{k>0}(-1)^n/(1+k^2π^2)$

answered Jul 23, 2017 at 5:03

9 votes

Accepted

Writing the Beta Function in terms of the Gamma Function

answered Mar 21, 2018 at 1:04

6 votes

prove the following algebraically $\left( \begin{array}{c} 2n \\ 2\ \end{array} \right) = 2 \left( \begin{array}{c} n \\ 2\ \end{array} \right) + n^2$

answered Feb 6, 2018 at 23:22

6 votes

Accepted

Evaluate $\lim_{h\to 0}\frac 1 h\int_{-\infty}^\infty g\left(\frac x h\right)f(x)\,\mathrm dx$

answered Dec 24, 2016 at 9:58

5 votes

Accepted

Prove that if $\sigma \in S_{n}$ then $\sigma \tau \sigma^{-1}=(\sigma(1)),\sigma(2),...,\sigma(k))$.

answered Mar 5, 2017 at 8:11

5 votes

$\lim_\limits{\sigma_A, \sigma_B \to \infty }e^{-\sigma_A-\sigma_B} \sum_{k=0}^{\infty} \frac{{\sigma_A}^k}{k!}\cdot\frac{{\sigma_B}^k}{k!}$

answered Dec 1, 2017 at 18:13

4 votes

Accepted

Computing Neural Network Gradients

answered Aug 10, 2018 at 0:55

4 votes

Accepted

Prove that the sequence $b_{n}=\frac{n^{2}}{n+1}$ is unbounded.

answered Feb 14, 2017 at 20:35

4 votes

Accepted

Can a triangle have a side length of zero?

answered Feb 17, 2017 at 1:27

4 votes

Easy way to find out limit of $a_n = \left (1+\frac{1}{n^2} \right )^n$ for $n \rightarrow \infty$?

answered May 16, 2017 at 23:30

4 votes

Accepted

Find all $x$ such that $x^{35} + 5x^{19} + 11x^3$ is divisible by 17.

answered Jul 25, 2017 at 23:03

4 votes

Accepted

To check whether given series is convergent or divergent

answered Nov 18, 2017 at 21:17

4 votes

Taylor inside an integral

answered Nov 20, 2017 at 19:37

3 votes

Show recursion in closed form

answered Nov 18, 2017 at 23:14

3 votes

Accepted

Integral $\int_0^\infty x^ne^{-\frac{x}{a}} dx$

answered Aug 6, 2017 at 1:43

3 votes

How to use Stirling's approximation for $(2n)!$ to get the simplified version of the formula?

answered Jul 23, 2017 at 8:21

3 votes

Proving that $\lim\limits_{(x,y) \to (0,0)} \frac{x^2y^3}{x^2+y^2}=0$

answered Oct 1, 2017 at 4:26

3 votes

Accepted

Confusion on taylor series for complex analysis

answered Mar 30, 2017 at 17:18

3 votes

In support vector machine, what is the intuition of finding the hyperplane?

answered Mar 30, 2017 at 17:47

3 votes

Accepted

The intersection of infinite and finite closed and bounded sets

answered Apr 26, 2017 at 8:09

3 votes

Accepted

Proof of Convolution Theorem for three functions, using Dirac delta

answered Mar 9, 2017 at 2:34

3 votes

find the integral $\int ^\infty_0e^{-xu}\frac{\sin u}{u}du$

answered May 1, 2018 at 6:04

3 votes

Evaluating $\lim_{(x,y) \to (\pi,0)} {\cos(x) + 1 + {y^2/2} \over (x - \pi)^2 + y^2}$

answered May 23, 2018 at 16:57

3 votes

Accepted

Understanding theorem 9.12 in Rudin's PMA

answered Jan 17, 2018 at 18:28

3 votes

Accepted

Series expansion of $\left(1 + x^2\right)^{-1/2}$

answered Mar 10, 2018 at 22:14

3 votes

Several ways to prove that $\sum\limits^\infty_{n=1}\left(1-\frac1{\sqrt{n}}\right)^n$ converges

answered Jan 5, 2019 at 10:04

2 votes

Prove that$\frac{x^{2^{k-1}}}{\left(1-x^{2^{k}}\right)}$= $\frac{1}{1-x^{2^{k-1}}}-\frac{1}{1-x^{2^{k}}}$

answered Jan 10, 2018 at 6:44

2 votes

Prove the convergence of $\int_1^{\infty} x^{-x}\,dx$

answered Apr 24, 2018 at 3:48

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154 Answers

Probability of getting a second $6$

Questions on proof of theorem 2.30 in Baby Rudin.

Calculate $∑_{k>0}(-1)^n/(1+k^2π^2)$

Writing the Beta Function in terms of the Gamma Function

prove the following algebraically $\left( \begin{array}{c} 2n \\ 2\ \end{array} \right) = 2 \left( \begin{array}{c} n \\ 2\ \end{array} \right) + n^2$

Evaluate $\lim_{h\to 0}\frac 1 h\int_{-\infty}^\infty g\left(\frac x h\right)f(x)\,\mathrm dx$

Prove that if $\sigma \in S_{n}$ then $\sigma \tau \sigma^{-1}=(\sigma(1)),\sigma(2),...,\sigma(k))$.

$\lim_\limits{\sigma_A, \sigma_B \to \infty }e^{-\sigma_A-\sigma_B} \sum_{k=0}^{\infty} \frac{{\sigma_A}^k}{k!}\cdot\frac{{\sigma_B}^k}{k!}$

Computing Neural Network Gradients

Prove that the sequence $b_{n}=\frac{n^{2}}{n+1}$ is unbounded.

Can a triangle have a side length of zero?

Easy way to find out limit of $a_n = \left (1+\frac{1}{n^2} \right )^n$ for $n \rightarrow \infty$?

Find all $x$ such that $x^{35} + 5x^{19} + 11x^3$ is divisible by 17.

To check whether given series is convergent or divergent

Taylor inside an integral

Show recursion in closed form

Integral $\int_0^\infty x^ne^{-\frac{x}{a}} dx$

How to use Stirling's approximation for $(2n)!$ to get the simplified version of the formula?

Proving that $\lim\limits_{(x,y) \to (0,0)} \frac{x^2y^3}{x^2+y^2}=0$

Confusion on taylor series for complex analysis

In support vector machine, what is the intuition of finding the hyperplane?

The intersection of infinite and finite closed and bounded sets

Proof of Convolution Theorem for three functions, using Dirac delta

find the integral $\int ^\infty_0e^{-xu}\frac{\sin u}{u}du$

Evaluating $\lim_{(x,y) \to (\pi,0)} {\cos(x) + 1 + {y^2/2} \over (x - \pi)^2 + y^2}$

Understanding theorem 9.12 in Rudin's PMA

Series expansion of $\left(1 + x^2\right)^{-1/2}$

Several ways to prove that $\sum\limits^\infty_{n=1}\left(1-\frac1{\sqrt{n}}\right)^n$ converges

Prove that$\frac{x^{2^{k-1}}}{\left(1-x^{2^{k}}\right)}$= $\frac{1}{1-x^{2^{k-1}}}-\frac{1}{1-x^{2^{k}}}$

Prove the convergence of $\int_1^{\infty} x^{-x}\,dx$