Simplify K!/(K+1)!
Simplify: $\frac{K!}{(K+1)! }$ I know that this simplifies to $\frac{1}{k+1}$, but I don't know how my professor does it. How would you go about solv...
Apr 19, 2026 1 VIEWS
Topic: General
5104 Articles 
Prove that $1^2+2^2+\cdots+n^2=\frac{n(n+1)(2n+1)}{6}$ for $n \in \mathbb{N}$.
Problem: Prove that $1^2+2^2+\cdots+n^2=\frac{n(n+1)(2n+1)}{6}$ for $n \in \mathbb{N}$. My work: So I think I have to do a proof by induction and I just w...
Apr 19, 2026 1 VIEWS
Finding Inverse of 2 (mod m)
Suppose $m$ is odd. What integer between $1$ and $m−1$ equals the inverse of $2 ($mod $m)$? What I have so far: Let $n$ be the inverse of $2 ($mod $m)$ wh...
Apr 19, 2026 1 VIEWS
Distinguishing between unimodal and bimodal normal data
I have a large number of data sets that have either a unimodal normal distribution or a bimodal normal distribution. I'm not a statistician by any me...
Apr 19, 2026 1 VIEWS
Mnemonic for Integration by Parts formula?
The Integration by Parts formula may be stated as: $$\int uv' = uv - \int u'v.$$ I wonder if anyone has a clever mnemonic for the above formula....
Apr 19, 2026 1 VIEWS
Smooth function with $f^{(n)}=0$ is polynomial
Let $I \subseteq \mathbb R$ be an interval and $f:I \to \mathbb R$ a function. Show that $f$ is a polynomial if and only if $f$ is smooth and there exists...
Apr 19, 2026 1 VIEWS
Set theory: difference between belong/contained and includes/subset?
This is a total noob question. I am reading Naive Set Theory by Paul R. Halmos, and I'm having difficulty to understand something which seems to be t...
Apr 19, 2026 1 VIEWS
Drawing a monkey saddle surface in matlab? [closed]
I'd like to draw a monkey saddle surface using matlab. But how do I plot a function of several variables in matlab? I never did that before. I can de...
Apr 19, 2026 1 VIEWS
What does the Hodge conjecture mean?
I read from the Internet that according to the Hodge conjecture, a certain harmonic differential form in a projective, non-singular algebraic variety is a...
Apr 19, 2026 1 VIEWS
What is reductive group intuitively?
I am studying Geometric invariant theory and wonder how I should understand linearly reductive algebraic group. We say that an affine algebraic group $G$ ...
Apr 19, 2026 1 VIEWS
What is mathematical research like?
I'm planning on applying for a math research program over the summer, but I'm slightly nervous about it just because the name math research soun...
Apr 19, 2026 1 VIEWS
Mean number density for normally distributed particles
Say we have a distribution for the density of particles in a region of space $$ n(x) = \frac{N}{\pi^{1/2} R} \textrm{e}^{-x^{2}/R^{2}} $$ where $R = \sqrt...
Apr 19, 2026 1 VIEWS