Jean-Claude Arbaut
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 18h revised Convergence: infinite series edited tags 18h answered Convergence: infinite series 19h comment Convergence: infinite series Intuitive hint: the inequality means that if $b_n$ decreases, then $a_n$ decreases more, and if $b_n$ increases, $a_n$ increases less. So, apart form the first term, you should expect that the finite sums of $a_n$ are less than the finite sums of $b_n$. You can factor out the first terms without changing the successive quotients, to make this more precise. 19h revised Is $\sum_{k=-\infty}^{0}f(-k)=\sum_{k=0}^{\infty} f(k)$ always? edited tags 19h comment Evaluation of $\int_{0}^{\frac{\pi}{4}}\left(\cos 2x \right)^{\frac{11}{2}}\cdot \cos xdx$ Nice answer, and nice LaTeX lesson ;-) 20h revised Evaluation of $\int_{0}^{\frac{\pi}{4}}\left(\cos 2x \right)^{\frac{11}{2}}\cdot \cos xdx$ added 692 characters in body 20h revised Evaluation of $\int_{0}^{\frac{\pi}{4}}\left(\cos 2x \right)^{\frac{11}{2}}\cdot \cos xdx$ added 692 characters in body 20h answered Evaluation of $\int_{0}^{\frac{\pi}{4}}\left(\cos 2x \right)^{\frac{11}{2}}\cdot \cos xdx$ 20h comment How do I find the determinants of $3A, -A, A^2, A^{-1}$, where A is an $4\times 4$ matrix and $\det(A) = \frac{1}{3}$? For the (2), you can also use the fact that it's a multilinear form. 21h revised Textbook +reference book in complex analysis added 11 characters in body 23h comment How prove that $\frac{1}{\sin^2\frac{\pi}{2n}}+\frac{1}{\sin^2\frac{2\pi}{2n}}+\cdots+\frac{1}{\sin^2\frac{(n-1)\pi}{2n}} =\frac{2}{3}(n-1)(n+1)$ This will be helpful: math.stackexchange.com/questions/544228/… 1d revised A math contest question related to Ramsey numbers edited tags 1d comment show that $(1 +\sin{A}) + \cos^2{A} = 2(1 + \sin{A})$? Wrong. Try substituting $A =\pi/2$. 1d comment Finding pattern @Chou But then no answer leaves this property true, since the only primes are $2,3,11$, and they are all divisible by $5$. 1d revised how to prove that a relation is antisymmetric? added 7 characters in body 1d revised how to prove that a relation is antisymmetric? added 22 characters in body 1d revised how to prove that a relation is antisymmetric? added 6 characters in body 1d answered how to prove that a relation is antisymmetric? 1d reviewed Reject To prove ($A\cup B$) $\cap C$ = $(A \cup C) \cap (B \cup C)$ 1d reviewed Close basic word problem!