I've seen that the Cesaro sum is $1/2$ but haven't been able to find the steps for figuring that out.

Is the following reasoning correct? $$-\csc2x = -1[\csc(2x)\cdot\cot(2x)] = -1[\csc(2x)\cdot\cot(2x)\cdot2\cdot2]$$ I am unsure whether that is correct so...

Two questions Let $R$ be commutative and have $1_R$. Two ideals are called coprime/comaxmal if $I + J = R$ (1) the above is equivalent to saying there exi...

$$\sinh(x) = \frac{1}{2(e^x - e^{-x})}$$ $$\cosh(x) = \frac{1}{2(e^x + e^{-x}}$$ $$\tanh(x) = \frac{\sinh (x)}{\cosh (x)}$$ Prove: $$\frac{d(\tanh(x))}{dx...

I am stuck on what seems to be an easy exercise. We have $f(x,y) = x^2 + 4xy + y^2 \mbox{ for all } (x,y)$ in $\mathbb{R}^2.$ Now we are supposed to find ...

http://www2.ift.ulaval.ca/~dadub100/cours/H09/22257/ntsLogique.pdf If you look in Annex B, I am allowed to use all laws from chapter 3 and below. https://...

Can someone help me with a approach? Not looking for a solution just for a hint

I was reading Gilbert Strang's book for Linear Algebra (along with his lectures) and I feel that he is emphasizing that the 4 fundamental subspaces (...

In this machine learning lecture the professor says: Suppose $\mathbf{X}\in\Bbb R^p$ and $g\in G$ where $G$ is a discrete space. We have a joint probabili...

This is the "symmetric form" of a line: $$\frac{x-x_1}{\sin\theta}=\frac{y-y_1}{\cos\theta}$$ where $\theta$ is inclination of the line. I know the equati...