Permutation: $$P(n,r) = \frac{n!}{(n-r)!}$$ Combination: $$C(n,r) = \frac{n!}{(n-r)!r!}$$ Apparently, you use combination when the order doesn't matt...

Are there rules for when small, capital and greek symbols are used? Simple example: The volume left in a cube with a sphere in it is V=C-S with capital st...

I'm would like to find the antiderivative of $$\frac{x^2}{(x-1)^5}$$ I tried without using partial fractions but I did not manage, so I started a les...

The question asks: Solve $$\log_5(x-1) + \log_5(x-2) - \log_5(x+6)= 0 $$ I know that according to log laws, addition with the same base is equal to multip...

In the context of real analysis, I have found this question: For each $$f \in C[0,1] $$ there is a series of even polynomials , which converge uniformly o...

Determine if the following function is odd or even using Fourier series. $$f(x)=x^5\sin x$$ If a function is even then $b_n=0$ and you have to evaluate $a...

This seems counterintuitive, but $22/7$ is closer to $\pi$ than $3.14=314/100$ which has a significantly greater denominator. Why is $22/7$ a better appro...

Does anyone know an efficient algorithm to compute all solutions of $$ x^2 + y^2 + z^2 + w^2 = p $$ where $x, y, z, w \in \mathbb{Z}$ and $p \in \mathbb{P...

Every finite-dimensional linear map can be represented by a matrix. But what about the opposite: Does every matrix correspond to a linear map?

Hi guys are there any other Methods/approach to simplify $k^2(k+1)^2 + 4(k+1)^3$ instead of expanding everything out and getting a quartic and cubic?? I e...