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comment How find the $x_{n}$ closed form,with $x_{n}=\{(a_{1},a_{2},\cdots,a_{n})|a_{i}a_{i+1}=0,\rm{and}~ a_{i}\in\{0,1\},\forall i=1,2,\cdots,n\}$
This is just the number of sequences of length $n$ without two consecutive ones. See here.
2d
revised solving the integral $\sqrt{\sin(y)}(4-y)$
deleted 2 characters in body; edited title
2d
comment question on linear algebra word problems.
What have you tried? Perhaps you should start by writing a linear equation, sales = m*advert + b and use the given data.
2d
revised question on linear algebra word problems.
added 5 characters in body
May
1
comment Unseen Theorem Based on parallelogram
When you say APQ = ABD, do you mean that the triangles are congruent and that AB = AQ and AD = AP?
Apr
27
answered Show that $\sin^2 \theta \cdot \cos^2\theta = (1/8)[1 - \cos(4 \theta)]$.
Apr
21
comment Flux of the amount of buffalo entering a square kilometer per minute
What book is this?
Apr
19
comment Mathematical Rigor in Proving Limits by $\epsilon-\delta$ Definition
I agree with grand_chat's answer, and also with the notational point made by Jon Warneke at the start of his answer.
Apr
18
answered Mathematical Rigor in Proving Limits by $\epsilon-\delta$ Definition
Apr
8
comment How do I find a basis of $\mathbb{Q}(i,\sqrt{2}+i,\sqrt{3}+i)$ over $\mathbb{Q}$?
@los_mathematiker Just prove both inclusions - they are both easy.
Mar
29
comment Journey with integer steps
Here's another way to think about it. Start with a regular $n$-gon with side length $1000000n$. Clearly you can add $1$ to one side and you'll still have an $n$-gon. Then add $2$ to the next side, and so on. Since the result is so close to a regular $n$-gon (it's only off by about one part in a million), it's pretty clear (intuitively, again) that this is possible.
Mar
29
comment $K \subset E \subset L$ finite field extensions and $L$ normal over $K$. Is $L$ normal over $E$, and is $E$ normal over $K$?
Try letting $L$ be the splitting field of, say, $x^3-2$ over $\mathbb{Q}$.
Mar
29
answered Journey with integer steps
Mar
24
awarded  Yearling
Mar
16
comment Quadratic equations - Fastest way to find the value of d
Well, now you can factor both quadratics on the right as well, and they have a common factor. That should make things much easier.
Mar
16
comment Quadratic equations - Fastest way to find the value of d
Both quadratics on the left factor, and have a common factor. Are you sure you entered the formulas correctly on the right-hand side?
Mar
12
comment Determine if $\sum_{t=1}^\infty (-1)^{n+1}\frac{(-4)^n}{n4^n}$ converges or diverges.
Or (my favorite proof), that the sum is $1+\frac{1}{2}+ \left(\frac{1}{3}+\frac{1}{4}\right) + \left(\frac{1}{5}+\frac{1}{6}+\frac{1}{7} + \frac{1}{8}\right) + \cdots > 1 + \frac{1}{2} + \frac{1}{2} + \frac{1}{2} + \cdots$.
Mar
7
comment Derivative of $x(x+2)^3$ in factored form don't see it
Factor out $(x+2)^2$ from each term.
Mar
4
comment Let $p$ a prime number, then prove that : $\sum \limits_{k=0}^{p} \binom {p}{k} \binom{p+k}{k} \equiv 2^p +1 \pmod{p^2}$
@Maman I'm not sure there is. I tried proving it directly, and ended up having to find $\sum 1\cdot 2\cdots \hat{i}\cdots (p-3)$, which is reminiscent of Wolstenholme's theorem.
Mar
4
answered Let $p$ a prime number, then prove that : $\sum \limits_{k=0}^{p} \binom {p}{k} \binom{p+k}{k} \equiv 2^p +1 \pmod{p^2}$