In my backstory, I was introduced to the geometric concept of infinity rather young, through reading about the inversive plane. In the course of learning ...

When I have a sum in the type of $\sum _{n=0}^{\infty }\:c_nx^n$ and for a given value of $x$ the sum is infinity (or converges to infinity? I am not sure...

I just have a question regarding how to define a truth set for the following: Suppose the domain is all integers Z, and the statement is true for all inte...

So I got that there is two cases: odd or even. If odd then say $n^2$ is $(2k+1)^2 = 4k^2 + 4k + 1.$ then $4k^2 + 4k + 1 + 5$ would need to be divisible by...

I need help solving this derivative using the chain rule. I have tried setting $u = -x^2$

Let $R=[-1,1]\times [-1,1]$ be a square in $\mathbb R^2$. Find the average squared distance of points in $R$ to the origin. My progress: I have learned ho...

I want to find the power series of $$f(x)=\frac{1}{x^2+x+1}$$ How can I prove the following? $$f(x)=\frac{2}{\sqrt{3}} \sum_{n=0}^{\infty} \mathrm{sin}\fr...

How to find the Rank of Operator A, acting in $\mathbb R^{2\times 2} \ $ by the rule: $$AX=\begin{pmatrix} 1 & 1 \\ 0 & 0 \end{pmatrix}X$$ I'...

The answer given is that it's not because it's a parabola and hence, would fail the horizontal line test, i.e., two values of $x$ will have the ...

This formula provides the $n$th term in the Fibonacci Sequence, and is defined using the recurrence formula: $u_n = u_{n − 1} + u_{n − 2}$, for $n > 1$...