User Math-fun - Mathematics Stack Exchange

14 votes

Memoryless property and geometric distribution

answered Dec 19, 2014 at 8:52

11 votes

How many ways can seven people sit around a circular table?

answered Dec 16, 2014 at 11:02

9 votes

How did Euler realize $x^4-4x^3+2x^2+4x+4=(x^2-(2+\alpha)x+1+\sqrt{7}+\alpha)(x^2-(2-\alpha)x+1+\sqrt{7}-\alpha)$?

answered Feb 15, 2015 at 22:32

9 votes

Proof of a Ramanujan Integral

answered Feb 18, 2015 at 18:09

9 votes

Compute $\int_{0}^{1} \frac{\ln(x)}{(x+1)^2} \mathrm dx$

answered Sep 10, 2015 at 18:00

9 votes

Accepted

Evaluate $\int_0^1 \frac{\log(1+x)}{x}$

answered Nov 25, 2016 at 8:48

8 votes

Why aren't the functions $f(x) = \frac{x-1}{x-1}$ and $f(x) = 1$ the same?

answered Jan 11, 2017 at 15:27

8 votes

Prove that $E(X) = \int_{0}^{\infty} P(X>x)\,dx = \int_{0}^{\infty} (1-F_X(x))\,dx$.

answered Mar 10, 2016 at 13:07

8 votes

Accepted

Series Approximation How to evaluate $1/3+1/3(1/3)^3+1/5(1/3)^5+...$?

answered Aug 18, 2015 at 10:20

8 votes

Accepted

If $\lim_{n\to\infty}\frac{1^a+2^a+...+n^a}{(n+1)^{a-1}.((na+1)+(na+2)+...+(na+n))}=\frac{1}{60}$, Find the value of a

answered Jul 22, 2015 at 19:50

8 votes

what is the expected value of $x^TAx$?

answered Jul 29, 2015 at 8:13

8 votes

I am trying to maximize an exponential function

answered Apr 7, 2015 at 14:54

8 votes

Why is $\int_0^{2\pi}{\sin x\over x}$ bigger than 0?

answered Jun 24, 2015 at 8:41

8 votes

Accepted

Finding $\lim_{n\to \infty}\frac{1}{n^2}\left(e^{1/n^2}+2e^{2^2/n^2}+\cdots+ne^{n^2/n^2}\right)$

answered Feb 2, 2020 at 14:16

7 votes

Accepted

Evaluate the sum $\sum_{n=0}^\infty \frac{x^{2n+1}}{(2n+1)!}$

answered Mar 15, 2015 at 22:44

7 votes

Negative binomial distribution - sum of two random variables

answered Dec 6, 2014 at 8:29

7 votes

Accepted

How to calculate \sqrt{7+2\sqrt{10} } =

answered Mar 30, 2016 at 12:39

7 votes

Accepted

$\lim_{n\to\infty }n\sin (\frac{1}{n^{2}+1})$

answered Nov 14, 2016 at 8:29

7 votes

Accepted

Help to prove that : $\int_{0}^{1}\int_{0}^{1}{1-x\over 1-xy}\cdot{x\over \ln{(xy)}}dxdy={1\over 2}\ln{1\over 2}$

answered Jan 3, 2017 at 8:08

6 votes

Accepted

CDF of max($X$, $Y$) - where is the mistake?

answered Jun 6, 2017 at 11:43

6 votes

Accepted

Solve the system $x^2-3xy+2y^2+x-y=0$, $2x^2-2xy-3y^2-2x+5y=0$

answered Aug 25, 2017 at 10:15

6 votes

What is the appropriate method to find the value of $1$ - $1\over 7$ + $1\over 13$ - ... upto infinite terms?

answered Sep 11, 2015 at 10:24

6 votes

Evaluation of $\int_0^1 \frac{x^3}{2(2-x^2)(1+x^2) + 3\sqrt{(2-x^2)(1+x^2)}}\,\mathrm dx$

answered Dec 15, 2014 at 16:45

6 votes

The sum of the squares is less than or equal to the square of the sums for all $n$

answered Mar 8, 2015 at 7:02

5 votes

Closed-form of integral $\int_0^1 \int_0^1 \frac{\arcsin\left(\sqrt{1-s}\sqrt{y}\right)}{\sqrt{1-y} \cdot (sy-y+1)}\,ds\,dy $

answered Dec 17, 2014 at 13:28

5 votes

Prove that, $(2\cdot 4 \cdot 6 \cdot ... \cdot 4000)-(1\cdot 3 \cdot 5 \cdot ...\cdot 3999)$ is a multiple of $2001$

answered Dec 9, 2014 at 10:18

5 votes

Implementing Ornstein–Uhlenbeck in Matlab

answered May 18, 2015 at 14:27

5 votes

Solving for n in the equation $\left ( \frac{1}{2} \right )^{n}+\left ( \frac{1}{4} \right )^{n}+\left ( \frac{3}{4} \right )^{n}=1$

answered Jun 8, 2015 at 14:44

5 votes

Accepted

Is there another simple way to solve this integral $I=\int\frac{\sin{x}}{\sin{x}+\cos{x}}dx$?

answered Jul 16, 2015 at 8:06

5 votes

Accepted

$\int\limits_{0}^{\pi/2}\frac{1+2\cos x}{(2+\cos x)^2}dx$

answered Aug 13, 2015 at 5:01

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348 Answers

Memoryless property and geometric distribution

How many ways can seven people sit around a circular table?

How did Euler realize $x^4-4x^3+2x^2+4x+4=(x^2-(2+\alpha)x+1+\sqrt{7}+\alpha)(x^2-(2-\alpha)x+1+\sqrt{7}-\alpha)$?

Proof of a Ramanujan Integral

Compute $\int_{0}^{1} \frac{\ln(x)}{(x+1)^2} \mathrm dx$

Evaluate $\int_0^1 \frac{\log(1+x)}{x}$

Why aren't the functions $f(x) = \frac{x-1}{x-1}$ and $f(x) = 1$ the same?

Prove that $E(X) = \int_{0}^{\infty} P(X>x)\,dx = \int_{0}^{\infty} (1-F_X(x))\,dx$.

Series Approximation How to evaluate $1/3+1/3(1/3)^3+1/5(1/3)^5+...$?

If $\lim_{n\to\infty}\frac{1^a+2^a+...+n^a}{(n+1)^{a-1}.((na+1)+(na+2)+...+(na+n))}=\frac{1}{60}$, Find the value of a

what is the expected value of $x^TAx$?

I am trying to maximize an exponential function

Why is $\int_0^{2\pi}{\sin x\over x}$ bigger than 0?

Finding $\lim_{n\to \infty}\frac{1}{n^2}\left(e^{1/n^2}+2e^{2^2/n^2}+\cdots+ne^{n^2/n^2}\right)$

Evaluate the sum $\sum_{n=0}^\infty \frac{x^{2n+1}}{(2n+1)!}$

Negative binomial distribution - sum of two random variables

How to calculate \sqrt{7+2\sqrt{10} } =

$\lim_{n\to\infty }n\sin (\frac{1}{n^{2}+1})$

Help to prove that : $\int_{0}^{1}\int_{0}^{1}{1-x\over 1-xy}\cdot{x\over \ln{(xy)}}dxdy={1\over 2}\ln{1\over 2}$

CDF of max($X$, $Y$) - where is the mistake?

Solve the system $x^2-3xy+2y^2+x-y=0$, $2x^2-2xy-3y^2-2x+5y=0$

What is the appropriate method to find the value of $1$ - $1\over 7$ + $1\over 13$ - ... upto infinite terms?

Evaluation of $\int_0^1 \frac{x^3}{2(2-x^2)(1+x^2) + 3\sqrt{(2-x^2)(1+x^2)}}\,\mathrm dx$

The sum of the squares is less than or equal to the square of the sums for all $n$

Closed-form of integral $\int_0^1 \int_0^1 \frac{\arcsin\left(\sqrt{1-s}\sqrt{y}\right)}{\sqrt{1-y} \cdot (sy-y+1)}\,ds\,dy $

Prove that, $(2\cdot 4 \cdot 6 \cdot ... \cdot 4000)-(1\cdot 3 \cdot 5 \cdot ...\cdot 3999)$ is a multiple of $2001$

Implementing Ornstein–Uhlenbeck in Matlab

Solving for n in the equation $\left ( \frac{1}{2} \right )^{n}+\left ( \frac{1}{4} \right )^{n}+\left ( \frac{3}{4} \right )^{n}=1$

Is there another simple way to solve this integral $I=\int\frac{\sin{x}}{\sin{x}+\cos{x}}dx$?

$\int\limits_{0}^{\pi/2}\frac{1+2\cos x}{(2+\cos x)^2}dx$