If we have $\Sigma\frac{1}{n}$, why do we say it is divergent? Yes, it is constantly increasing, but after a certain point, $n$ will be so large that we w...

I have found an algorithm called the Binary GCD/Stein Algorithm which takes two non-negative integers and finds the greatest common factor of the two. Wha...

\begin{align} \phi^5 &= 11,\underline{0}901699\cdots\\ \phi^6 &= 17,\underline{9}44271\cdots\\ \phi^7 &= 29,\underline{6}34441\cdots\\ \phi^8 ...

How can someone prove in Euclidean geometry that the statement "A line connecting an interior and an exterior point of a circle should intersect the circl...

I once had an argument with a professor of mine, if the following definition was a recursive or inductive definition: Suppose you have sequence of real nu...

Problem: Find the area of a regular hexagon whose sides measures 5 cm Sol'n 1: I can cut the hexagon into 6 small triangles, so the area of triangle ...

How can I show that the Fourier transform of an even integrable function $f\colon \mathbb{R}\to\mathbb{R}$ is even real-valued function? And the Fourier t...

I am confused on how to find the splitting field of a polynomial. For example, consider the polynomial $$p(x)=x^2+2.$$ I know that the splitting field is ...

I am attempting to solve the problem $$\int \frac{dx}{x^2+x+1}$$ First, I complete the square, then factor out a $\frac {3}{4}$: $$\int \frac{dx}{\frac{3}...

What is the formula for the birthday problem? I can't seem to find JUST the formula. I don't care how it works at this point, I just want to kno...