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Mar
21
comment What is the probability that a point chosen randomly from inside an equilateral triangle is closer to the center than to any of the edges?
I like this solution because it makes it clear why the answer is a rational number. From the calculus-based answer this seems a bit mysterious.
Mar
16
comment When is $\binom{2n}{n}\cdot \frac{1}{2n}$ an integer?
Also see oeis.org/A067348 , which is double this sequence by definition.
Mar
11
answered What is the limit of (Odd Numbers Product) / (Even Number Product)
Mar
11
revised How to prove that $\forall n \in \Bbb{N}$, $n+\lfloor \sqrt{n} +\frac12 \rfloor$ cannot be a complete square?
edited tags
Mar
10
comment How to integrate when two functions are being multiplied by each other?
You want "integration by parts".
Mar
10
comment A five-digit number whose square has its last five digits equal to the number.
That's right. I did it for $k = 2$ because doing it for $k = 1$ seemed trivial.
Mar
10
answered Log-concave function changes when scalar is added
Mar
10
answered A five-digit number whose square has its last five digits equal to the number.
Mar
10
answered Factoring Numbers with inner nulls
Mar
10
revised Find the moment generating function, mean, and variance of the piecewise function
improved formatting
Mar
7
comment $N=(x^2-1)(y^2-1)$ has more than one solution
oeis.org/A063067 gives a list of such numbers (if you find the first three solutions 360, 504, 2304 by brute force you can find this list). That provides a link to the following notes: mathpages.com/home/kmath275.htm
Feb
26
comment How to prove that if $S(n)$ is triangular number for $n \in Z_{+}$, then $a=9 $?
Perhaps relevant: $S(2)$ is triangular if and only if $a$ is in the sequence at oeis.org/A216134 $(1, 4, 9, 26, 55, \ldots)$. I also find the sporadic solutions $a = 2, 23$ for $n = 3$ and no others for $n \le 5, a \le 10^7$.
Feb
25
comment Find two vectors in $P$ and check that their sum is not in $P$.
That's right. What's more, that will hold for any plane $P$ that doesn't pass through the origin.
Feb
25
answered Find two vectors in $P$ and check that their sum is not in $P$.
Feb
24
answered If $X $ is distributed as $ U(0,1)$ what is the distribution of $Y = X^3$?
Feb
24
comment Solve $\lim_{n\to \infty}\left(\frac{1}{n+1}+\frac{1}{n+2}+\cdots+\frac{1}{n+n}\right)$ without using Riemann sums.
How do you get that $\lim_{n \to \infty} H_n - \log n - \gamma = 0$ without using Riemann sums?
Feb
23
answered An example that a 2D shape with its centre of mass on its boundary
Feb
18
answered What's the chance of drawing 8 or more cards of one suit if you draw 26 cards from a deck?
Feb
17
answered Prove the following trigonometric identity without a calculator involved
Feb
17
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