User Donald Splutterwit

6 votes

Dividing a rectangle into 4 parts in the ratio 1:2:3:4, with only 2 lines

answered Feb 9, 2018 at 10:59

6 votes

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

answered Feb 2, 2018 at 15:29

6 votes

Solve $\sum_{k=0}^{\infty}\frac{1}{1-16k^2}$

answered Apr 3, 2017 at 19:14

6 votes

Find the curve of intersection between $x^2 + y^2 + z^2 = 1$ and $x+y+z = 0$

answered Aug 11, 2017 at 19:34

6 votes

Peculiar Sum regarding the Reciprocal Binomial Coefficients

answered Jul 24, 2017 at 18:05

6 votes

Expectation of a die roll summed

answered Aug 6, 2017 at 22:48

6 votes

Accepted

Calculate $\tan^2{\frac{\pi}{5}}+\tan^2{\frac{2\pi}{5}}$ without a calculator

answered Jun 25, 2017 at 23:14

6 votes

Find Maclaurin series of $f(x)=\int_0^x \frac{\ln(1-t^2)}{t}\, dt$.

answered Jun 18, 2017 at 19:53

6 votes

How to prove the equality $a_n = n^2$ for every $n$, if $n \in \mathbb N$?

answered Nov 24, 2017 at 0:37

6 votes

Accepted

Simplify long expression

answered Oct 2, 2017 at 8:48

6 votes

Accepted

Fill out a group table with 6 elements

answered Oct 2, 2017 at 15:19

6 votes

Accepted

How do I prove that that $n \geq \log_2(n) ^{(\log_2(\log_2(n))}$ as n becomes large?

answered Sep 1, 2017 at 21:37

5 votes

Accepted

Find the coefficient of $x^9$ in the expansion of $(1+9x+27x^2+27x^3)^6$

answered Oct 7, 2019 at 20:17

5 votes

Accepted

Number of distinct functions such that there does not exist any $i\in A$ such that $f(i)=i+1$?

answered Aug 1, 2019 at 22:04

5 votes

Accepted

A clarification on the series expansion of $\cos(\sin(x))$

answered Nov 29, 2019 at 0:41

5 votes

Finding total number of possible numbers using below condition

answered Dec 3, 2019 at 16:10

5 votes

Accepted

Proof for $\sum_{i=0}^n \frac{n \choose i}{{2n-1} \choose i} = 2$.

answered Dec 4, 2019 at 19:14

5 votes

Accepted

Integral $\int_0^1 \frac{x\ln\left(\frac{1+x}{1-x}\right)}{\left(\pi^2+\ln^2\left(\frac{1+x}{1-x}\right)\right)^2}dx$

answered Oct 2, 2018 at 1:31

5 votes

Accepted

Summation of: (binomial coefficients * Stirling numbers of the second kind)

answered Jan 16, 2019 at 22:03

5 votes

Show if a graph can be written as Cartesian product

answered Mar 3, 2019 at 20:58

5 votes

Accepted

An Addition formula for Hermite polynomials

answered Oct 4, 2018 at 21:38

5 votes

Accepted

$\frac{a^2} {1+a^2} + \frac{b^2} {1+b^2} + \frac{c^2} {1+c^2} = 2.$ Prove $\frac{a} {1+a^2} + \frac{b} {1+b^2} + \frac{c} {1+c^2} \leq \sqrt{2}.$

answered Jun 17, 2018 at 19:46

5 votes

A system of logarithmic equations with parameters

answered Jun 21, 2018 at 19:16

5 votes

Accepted

Spivak's Calculus: Finding the formula for the sum of a series.

answered Jun 6, 2018 at 20:33

5 votes

Accepted

show by induction that $4^{2n+1}+3^{n+2}$ is divisible by $13$

answered Dec 2, 2020 at 1:35

5 votes

How many sets of non-adjacent edges in the 600-cell?

answered Nov 4, 2022 at 0:17

5 votes

Compute the following summation

answered Jan 9 at 20:45

5 votes

Looking for a proof of two combinatorial summation identities

answered Dec 21, 2020 at 0:40

5 votes

Any "shortcuts" to proving that $\frac{\sin(x)}2+\sin^2(\frac x2)\tan(\frac x2)\to\tan(\frac x2)$

answered Sep 28, 2020 at 19:18

5 votes

The identity $\arctan(x) + \arctan(x^3) = \arctan(2x+\sqrt{3}) + \arctan(2x-\sqrt{3})$

answered Sep 28, 2020 at 13:32

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1,386 Answers

Dividing a rectangle into 4 parts in the ratio 1:2:3:4, with only 2 lines

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

Solve $\sum_{k=0}^{\infty}\frac{1}{1-16k^2}$

Find the curve of intersection between $x^2 + y^2 + z^2 = 1$ and $x+y+z = 0$

Peculiar Sum regarding the Reciprocal Binomial Coefficients

Expectation of a die roll summed

Calculate $\tan^2{\frac{\pi}{5}}+\tan^2{\frac{2\pi}{5}}$ without a calculator

Find Maclaurin series of $f(x)=\int_0^x \frac{\ln(1-t^2)}{t}\, dt$.

How to prove the equality $a_n = n^2$ for every $n$, if $n \in \mathbb N$?

Simplify long expression

Fill out a group table with 6 elements

How do I prove that that $n \geq \log_2(n) ^{(\log_2(\log_2(n))}$ as n becomes large?

Find the coefficient of $x^9$ in the expansion of $(1+9x+27x^2+27x^3)^6$

Number of distinct functions such that there does not exist any $i\in A$ such that $f(i)=i+1$?

A clarification on the series expansion of $\cos(\sin(x))$

Finding total number of possible numbers using below condition

Proof for $\sum_{i=0}^n \frac{n \choose i}{{2n-1} \choose i} = 2$.

Integral $\int_0^1 \frac{x\ln\left(\frac{1+x}{1-x}\right)}{\left(\pi^2+\ln^2\left(\frac{1+x}{1-x}\right)\right)^2}dx$

Summation of: (binomial coefficients * Stirling numbers of the second kind)

Show if a graph can be written as Cartesian product

An Addition formula for Hermite polynomials

$\frac{a^2} {1+a^2} + \frac{b^2} {1+b^2} + \frac{c^2} {1+c^2} = 2.$ Prove $\frac{a} {1+a^2} + \frac{b} {1+b^2} + \frac{c} {1+c^2} \leq \sqrt{2}.$

A system of logarithmic equations with parameters

Spivak's Calculus: Finding the formula for the sum of a series.

show by induction that $4^{2n+1}+3^{n+2}$ is divisible by $13$

How many sets of non-adjacent edges in the 600-cell?

Compute the following summation

Looking for a proof of two combinatorial summation identities

Any "shortcuts" to proving that $\frac{\sin(x)}2+\sin^2(\frac x2)\tan(\frac x2)\to\tan(\frac x2)$

The identity $\arctan(x) + \arctan(x^3) = \arctan(2x+\sqrt{3}) + \arctan(2x-\sqrt{3})$