Convergence tests for a complex series?
For $\sum_{i=1}^{\infty} z_i$, where $z_i \in \mathbb{C}$, how should the convergence tests be performed? I read somewhere that the tests applied for conv...
Apr 22, 2026 1 VIEWS
Topic: General
5104 Articles 
Proving injective (1-1) using contrapositive
Given function $f:\mathbb Z \to \mathbb Z$ defined by $f(n) = n - 6$ $\mathbb Z$ in this case is the set of integers. Suppose for $x_1$, $x_2 \in \mathbb ...
Apr 22, 2026 1 VIEWS
Generalized binomial theorem
Prove that: $$(1+x)^{\alpha}=\sum_{n=0}^{+\infty}{\alpha \choose n} x^n$$ for $x\in[0;1), \alpha \in\mathbb{R}$ based on Taylor's theorem with Lagran...
Apr 22, 2026 2 VIEWS
Why is a square a bipartite graph?
From what I understand, a bipartite graph is a graph such that it can be divided into two disjoint sets of vertices, with each vertex in one set connectin...
Apr 22, 2026 2 VIEWS
What does 9P2 mean, and how would one solve it?
We are studying "Sequences, Series, and Probability" and it likely related to binomial theorem and pascals triangle. I've a test tomorrow morning, an...
Apr 22, 2026 1 VIEWS
Why are orthogonal projection matrices not ... orthogonal?
I know that given an orthogonal matrix U, then orthogonal projection onto the column space of U is represented by the matrix $UU^t$, which is again orthog...
Apr 22, 2026 2 VIEWS
How to calculate the length of the sides of a rectangle given the diagonal coordinates
I have the top left corner and bottom right corner coordinates of a rectangle. The length of the diagonal is just the distance between the top left corner...
Apr 22, 2026 1 VIEWS
Factor $14x^2 - 17x + 5$.
Objective: To factor general quadratic trinomials with integral coefficients. If $ax^2 + bx + c$, $(a>1)$ can be factored, the factorization will have ...
Apr 22, 2026 1 VIEWS
Use first derivative test to find local minima and local maxima
Use the First Derivative Test to find the points of local maxima and minima of the function $ƒ(x)=2x^3−x^4$. To begin we have $f'(x)=6x^2-4x^3$ Then ...
Apr 22, 2026 1 VIEWS
How to evaluate GF(256) element
I wonder is there any easy way to evaluate elements of GF$(256)$: meaning that I would like to know what $\alpha^{32}$ or $\alpha^{200}$ is in polynomial ...
Apr 22, 2026 1 VIEWS
Reverse Product Rule ODE
I don't understand the reverse product rule. When using integrating factors to solve the ODE below, $$\frac{dy}{dx} + \frac{2x}{1+x^2} y = \frac{4}{(...
Apr 22, 2026 1 VIEWS
What is the ordinary definition of a saddle-point?
Suppose $f:\mathbb{R}^2 \to\mathbb{R}$ is a $\mathcal{C}^2$ function such that both first-order partial derivatives vanish at the origin. Under what circu...
Apr 22, 2026 1 VIEWS