Donald Splutterwit's user avatar
Donald Splutterwit's user avatar
Donald Splutterwit's user avatar
Donald Splutterwit
  • Member for 6 years, 9 months
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81 votes

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

55 votes

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

35 votes
Accepted

Why do these paths all have the same length?

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.

18 votes

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

17 votes
Accepted

Sphere inside of a Sphere

16 votes

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

15 votes

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

14 votes

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

13 votes

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

13 votes
Accepted

Minimum of the given expression

12 votes
Accepted

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

12 votes

Iterative calculation of mean and standard deviation

10 votes
Accepted

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

10 votes

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

10 votes

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

10 votes

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

9 votes

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

9 votes
Accepted

Combinatorial proof of Negative Binomial Identity $(1+x)^{-n}= \sum_{k=0}^{\infty} (-1)^k \binom{n+k-1}{k} x^k$

9 votes

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

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 $z=\alpha$, $\beta$, $\gamma$, $\delta$

9 votes
Accepted

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

8 votes

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

8 votes

Need help figure out a Fibonacci related math trick

8 votes
Accepted

Binomial theorem relating proof

7 votes

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

7 votes
Accepted

Exponential generating function of the falling factorial

7 votes

I need help proving an inequality by induction

7 votes
Accepted

Laguerre polynomial question

7 votes
Accepted

Prove that $\sum _{k=1}^{n-1} \binom{n-1}{k} k^{k-1} (n-k)^{n-k-1}=n^{n-1}-n^{n-2}$

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