rogerl
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 14h 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 : $\sum \limits_{k=0}^{p} \binom {p}{k} \binom{p+k}{k} \equiv 2^p +1 \pmod{p^2}$