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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
May
14
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.
May
14
comment Computing a certain $2014$-fold product using a particular associative binary operation $\ast$
@FlorinM. You also need the fact that it's commutative.
May
10
reviewed Approve Determine all natural numbers n and m that satisfying in this equation.
May
10
reviewed No Action Needed Proof of Cauchy Riemann Equations in Polar Coordinates
May
4
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
Apr
30
revised Probability problem without the usual information
deleted 3 characters in body; edited title
Apr
25
revised Convergence: infinite series
edited tags
Apr
25
answered Convergence: infinite series
Apr
25
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.
Apr
25
revised Is $\sum_{k=-\infty}^{0}f(-k)=\sum_{k=0}^{\infty} f(k)$ always?
edited tags