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 17h comment Hessian-Matrix positive definite $\iff$ $a$ local minimum? Try $f(x,y)=x^4+y^4$ at $x=y=0$. 17h revised Hessian-Matrix positive definite $\iff$ $a$ local minimum? added 2 characters in body 17h answered How to do this triangle question? 17h reviewed Reopen Best way to find Residue? 18h comment Fibonacci-related infinite sum For the first, this and this give a reference to an article of Edmund Landau which is here pp. 298-300 (in french). 18h comment Fibonacci-related infinite sum Not completely unrelated : mathoverflow.net/questions/51426/… 18h comment Inductively prove that any natural number $\ge 12$ can be written as the sum of 4s and 5s Notice that the set $S$ of numbers $n\geq12$ that cannot be written $n=4a+5b$ is either empty, either has a minimum element $n_0$ (since $S$ is then a nonempty set of nonnegative integers, or a subset of $\Bbb N$, which is well ordered). But then $n_0$ must be $\leq15$, otherwise one of $n_0-4$ or $n_0-5$ would be in $S$, contradiction. Thus you just have to check $12,13,14,15$. Almost the same argument will give you an induction proof. 18h comment Sum of zeros of $P(x)$ Statement of the problem (#10) and related discussion on Art of Problem Solving. Since you wrote the same question there, it's nice to tell :) 18h revised Sum of zeros of $P(x)$ edited tags 18h comment How does $\cos (2z) = e^{2zi}$? @snowman sine is odd May14 comment Probability of dice with a cumulative successes Do you mean that according to his skill, the attacker will roll 1, or 2 or .. or 5 dice? And for each outcome that is 9 or 10, he will roll another die? Then, does this apply to the additionnal dice (I mean, if he gets 9 or 10 on the 6th die, he will throw yet another die). Anyway, you have to know the "base" number of dice (between 1 to 5) to compute the probability to win. With only one die for example, the attacker can't win with more than 1 success, obviously. May14 comment Computing a certain $2014$-fold product using a particular associative binary operation $\ast$ @FlorinM. You also need the fact that it's commutative. May10 reviewed Approve Determine all natural numbers n and m that satisfying in this equation. May10 reviewed No Action Needed Proof of Cauchy Riemann Equations in Polar Coordinates May4 revised 5 pears and 1 apple cost as much as 2 pears and 2 apples. If each apple costs $0.75,find the total cost of 100 pears and 450 apples. edited tags Apr30 revised Probability problem without the usual information deleted 3 characters in body; edited title Apr25 revised Convergence: infinite series edited tags Apr25 answered Convergence: infinite series Apr25 comment Convergence: infinite series Intuitive hint: the inequality means that if$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$. You can factor out the first terms without changing the successive quotients, to make this more precise. Apr25 revised Is$\sum_{k=-\infty}^{0}f(-k)=\sum_{k=0}^{\infty} f(k)\$ always? edited tags