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Derivative of binomial coefficients
I obtained the following formula in Mathematica: $$\frac{d}{dn}\ln\binom{n}{k} = H_{n} - H_{n-k}$$ where $H_n$ are the harmonic numbers ($H_n = \sum_{i=1}...
Apr 16, 2026
Archive: Updates
updates
Can a non-extreme point be an optimal solution of a Linear Programming problem?
Consider a linear programming problem. Is it possible for an optimal solution to exist, but not at an extreme point? According to Bertsimas & Tsitsika...
Apr 16, 2026
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Graph Theory: Euler Trail and Euler Graph
- Background Information: I am studying graph theory in discrete mathematics. As I was reading my notes, I came across few definitions. I think I have not...
Apr 16, 2026
updates
The "Paradox" of Hilbert's Hotel
I'm not a mathematician at all. From this I read a sentence like this : A. Imagine a Grand Hotel with a (countably) infinite number of floors and roo...
Apr 16, 2026
updates
Evaluating a common integral for $\arcsin(x)$ using a different method
The common method of evaluating the integral below is by using the substitution $x = a \sin u$ which gives: $$\int\frac{dx}{\sqrt{a^2-x^2}}= \arcsin\Bigl(...
Apr 16, 2026
updates
Why do we use n-dimensional spaces?
On mathoverflow, Terry Tao says the following: For instance, one can view a high-dimensional vector space as a state space for a system with many degrees ...
Apr 16, 2026
![negative number divided by positive number, what would be remainder? [closed]](https://news.conceivablytech.com/uploads/negative-number-divided-by-positive-number-what-would-be-remainder-closed_720.jpg)
updates
negative number divided by positive number, what would be remainder? [closed]
my question is If $-27$ is divided by $5$, what would be the remainder?
Apr 16, 2026
updates
Is there a general solution for the "Spider and the Fly Problem"?
(I would be appreciative if somebody could give a more formal formulation of this problem.) The Spider and the Fly Problem is a problem in which the objec...
Apr 16, 2026
updates
Finite sequence
A finite sequence of numbers is called AWESOME if each subsequent member of the sequence, except the first one, is larger than the previous one and if the...
Apr 16, 2026
updates
Write 22 correct to 2 decimal places.
The book says 22.00 but surely one can't go ahead and write this number correct to 2 decimal places as we don't know what they are. Unless it is...
Apr 16, 2026
