(1) Find the sum of the power series $$\sum_{n=1}^{\infty} nx^n$$ (2) Find the sum of the series $$\sum_{n=1}^{\infty} \frac{n}{3^n}$$ Any tips on solving...

I'm looking for a way to express A being true does not imply B. I know that A implies B can be written as $A \rightarrow B$, but what about A does no...

This is not a technical question at all, but I'm quite confused about what should I use to compute volumes in $\mathbb{R}^3$ with integration. I'...

First we are given: $$\int_0^t H(s)\,ds=\left.\begin{cases} 0 & t<0\\ t & t>0\\ \end{cases}\right\}=tH(t).$$ Now I have attempted to do the ...

In Jónsson and Tarski's (1951) paper Boolean Algebras with Operators, Part I from the American Journal of Mathematics, they write formulae such as $L...

I know how you find out the Area of a Sector and the Arc Length but I'm not sure how to find out the radius of a circle? I understand that there are ...

I'm working on the following problem and could use some help. Unless I'm not making a connection to material covered in my course, we haven'...

Let $P(x)$ be a polynomial with integer coefficients such that $P(p)$ is prime for all prime $p$. What are all possible polynomials $P(x)$? Certainly $P(x...

For some reason I have not been able to find a straight answer to this. We know that $\frac{d}{dx}x^n=nx^{n-1}$ And this is true for $n=-1$ and $n=1$ $\im...

I've been solving initial value problems but this one has me stumped. So far what I have is that the position when r(0) is $(8,6,5)$ My next given is...