User Donald Splutterwit

81 votes

Can we calculate $ i\sqrt { i\sqrt { i\sqrt { \cdots } } }$?

answered Mar 1, 2018 at 21:19

55 votes

Prove that every positive integer divides a number such as $70, 700, 7770, 77000$.

answered Oct 8, 2017 at 20:06

35 votes

Accepted

Why do these paths all have the same length?

answered Jan 26, 2018 at 20:02

21 votes

If $u_1=1$ and $u_{n+1} = n+\sum_{k=1}^n u_k^2$, then $u_n$ is never a square.

answered May 14, 2019 at 0:18

18 votes

How to find $x$ given $\log_{9}\left(\frac{1}{\sqrt3}\right) =x$ without a calculator?

answered Nov 3, 2017 at 1:27

17 votes

Accepted

Sphere inside of a Sphere

answered Dec 9, 2019 at 23:20

16 votes

There is a number divisible by all integers from 1 to 200, except for two consecutive numbers. What are the two?

answered Nov 14, 2019 at 23:55

15 votes

How many pairs of numbers are there so they are the inverse of each other and they have the same decimal part?

answered Feb 25, 2017 at 20:05

14 votes

What's the expected number of times I have to roll two die until they both sum $7$?

answered Feb 2, 2018 at 20:19

13 votes

Solve the system of equations for $\sqrt{xy}$

answered Jan 3, 2021 at 17:40

13 votes

Accepted

Minimum of the given expression

answered Jul 28, 2017 at 13:47

12 votes

Iterative calculation of mean and standard deviation

answered Feb 17, 2017 at 16:04

12 votes

Accepted

Transforming a 8x8, 4x4 and 1x1 square into a 9x9 square

answered Oct 2, 2017 at 7:52

10 votes

Accepted

Conjecture: $\sum\limits_{n\geq0}\left(\frac12\right)^n\prod\limits_{k=1}^{n}\frac{2n-2k+1}{2n-2k+2}=\sqrt2$

answered Jan 20, 2019 at 22:35

10 votes

How do you simplify an expression involving fourth and higher order trigonometric functions?

answered Oct 9, 2017 at 1:43

10 votes

How can I find a bound for $\frac{n}{1} +\cdots+ \frac{n}{n}$ given $n< 10^{18}$?

answered Jun 25, 2017 at 21:19

10 votes

Number of ways to color the edges of a tetrahedron with two colors?

answered Feb 17, 2018 at 18:47

9 votes

A direct proof for $\int_0^x \frac{- x \ln(1-u^2)}{u \sqrt{x^2-u^2}} \, \mathrm{d} u = \arcsin^2(x)$

answered Jun 28, 2018 at 23:34

9 votes

An expression in rational numbers $x, y,$ and $z$: Why is it a square of a rational number?

answered Sep 19, 2020 at 15:46

9 votes

Value of $(\alpha^2+1)(\beta^2+1)(\gamma^2+1)(\delta^2+1)$ if $z^4-2z^3+z^2+z-7=0$ for $z=\alpha$, $\beta$, $\gamma$, $\delta$

answered Oct 8, 2017 at 16:31

9 votes

Accepted

Prove by induction: $2^{n+2} +3^{2n+1}$ is divisible by $7$ for all $n \in \mathbb{N}$

answered Sep 13, 2017 at 10:23

8 votes

Prove that $\left(1+\frac1 n\right)^n > 2$

answered Jul 17, 2018 at 0:07

8 votes

Accepted

Combinatorial proof of Negative Binomial Identity

answered Jul 18, 2018 at 19:37

8 votes

Need help figure out a Fibonacci related math trick

answered Sep 5, 2019 at 20:16

8 votes

Accepted

Binomial theorem relating proof

answered Oct 3, 2017 at 19:33

7 votes

Let $a \in G$ and suppose $aH = Hb$ for some $b \in G$. Then $aH=Ha$?

answered May 30, 2019 at 19:30

7 votes

Accepted

Exponential generating function of the falling factorial

answered Nov 25, 2019 at 0:26

7 votes

I need help proving an inequality by induction

answered Nov 25, 2019 at 11:51

7 votes

Accepted

Evaluate $\int_{1/2014}^{2014} \frac{\tan^{-1}x}{x}dx$ using Differentiation Under the Integral Sign

answered May 8, 2018 at 19:35

7 votes

Accepted

Prove $\sec^2\frac{\pi}{7}+\sec^2\frac{2\pi}{7}+\sec^2\frac{3\pi}{7}=24$ using the roots of a polynomial

answered Jun 3, 2018 at 22:49

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1,385 Answers

Can we calculate $ i\sqrt { i\sqrt { i\sqrt { \cdots } } }$?

Prove that every positive integer divides a number such as $70, 700, 7770, 77000$.

Why do these paths all have the same length?

If $u_1=1$ and $u_{n+1} = n+\sum_{k=1}^n u_k^2$, then $u_n$ is never a square.

How to find $x$ given $\log_{9}\left(\frac{1}{\sqrt3}\right) =x$ without a calculator?

Sphere inside of a Sphere

There is a number divisible by all integers from 1 to 200, except for two consecutive numbers. What are the two?

How many pairs of numbers are there so they are the inverse of each other and they have the same decimal part?

What's the expected number of times I have to roll two die until they both sum $7$?

Solve the system of equations for $\sqrt{xy}$

Minimum of the given expression

Iterative calculation of mean and standard deviation

Transforming a 8x8, 4x4 and 1x1 square into a 9x9 square

Conjecture: $\sum\limits_{n\geq0}\left(\frac12\right)^n\prod\limits_{k=1}^{n}\frac{2n-2k+1}{2n-2k+2}=\sqrt2$

How do you simplify an expression involving fourth and higher order trigonometric functions?

How can I find a bound for $\frac{n}{1} +\cdots+ \frac{n}{n}$ given $n< 10^{18}$?

Number of ways to color the edges of a tetrahedron with two colors?

A direct proof for $\int_0^x \frac{- x \ln(1-u^2)}{u \sqrt{x^2-u^2}} \, \mathrm{d} u = \arcsin^2(x)$

An expression in rational numbers $x, y,$ and $z$: Why is it a square of a rational number?

Value of $(\alpha^2+1)(\beta^2+1)(\gamma^2+1)(\delta^2+1)$ if $z^4-2z^3+z^2+z-7=0$ for $z=\alpha$, $\beta$, $\gamma$, $\delta$

Prove by induction: $2^{n+2} +3^{2n+1}$ is divisible by $7$ for all $n \in \mathbb{N}$

Prove that $\left(1+\frac1 n\right)^n > 2$

Combinatorial proof of Negative Binomial Identity

Need help figure out a Fibonacci related math trick

Binomial theorem relating proof

Let $a \in G$ and suppose $aH = Hb$ for some $b \in G$. Then $aH=Ha$?

Exponential generating function of the falling factorial

I need help proving an inequality by induction

Evaluate $\int_{1/2014}^{2014} \frac{\tan^{-1}x}{x}dx$ using Differentiation Under the Integral Sign

Prove $\sec^2\frac{\pi}{7}+\sec^2\frac{2\pi}{7}+\sec^2\frac{3\pi}{7}=24$ using the roots of a polynomial