Are there any useful identities for quickly calculating the sum of consecutive logs? For example $\sum_{k=1}^{N} log(k)$ or something to this effect. I sh...

This is my first question on the Mathematics section of StackExchange, so please forgive me if I don't follow all the rules or things like that. Here...

Say I had a quadrilateral and was given sides of length $a,b,c$ and diagonals $d,e.$ How can I find the fourth side? Let the fourth side be $x$. I though ...

Represent the function $f(x)= x^{0.5}$ as a power series: $\displaystyle \sum_{n=0}^\infty c_n(x−6)^n$ Got that: $c_0$ = $\sqrt{6}$ $C_1=\dfrac{1}{2\sqrt{...

how would I write the domain of this function? Would I ignore the part of the graph with the open circles like this? $\{x \ \ / \ -4 \leq x \leq -2 \text{...

Integrate: $$\int x \cos(x) \sin(x) \;dx$$ I've been trying to integrate by parts, but I can't! I know there's a trigonometric function abo...

find an equation for the tangent plane at the point (1,-1,4) for the surface given by $$z^2-2x^2-2y^2-12=0$$ my answer/work: $$<-4x,-4y,2z>$$ plug i...

Given symmetric positive semidefinite matrix $A$, let $$F(x) := x^TAx + b^Tx + c$$ Can someone show that $F$ is convex using the definition (without takin...

In light of that problem, I would like to offer my version. It could have puzzled both the American and Russian students:- ABCD is a parallelogram with th...

I was looking at how to do mathematical induction. One source said to use $n = 1$ for the basis step. But I have seen other sources choose the value $n = ...