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visits member for 4 years, 2 months
seen Oct 18 at 2:47

Don't have much time these days...


Sep
30
comment If $\displaystyle\lim_{n\to\infty}{\dfrac{a_n}{1+|a_n|}}=0$ then $\displaystyle\lim_{n\to\infty}{a_n}=0$
If $b_n = \frac{|a_n|}{1+|a_n|}$ then can you write $|a_n|$ in terms of $b_n$?
Aug
26
comment Root Calculation by Hand
@MonK: You can compute it by hand. For instance: en.wikipedia.org/wiki/Long_division.
Aug
19
comment What algorithm is used by computers to calculate logarithms?
@Cruncher: Thanks! I will try to find alternatives...
Jul
28
comment How prove $\sqrt{r^2+c^2}$ is irrational
Tagging this is elementary-number-theory until proven otherwise.
Jul
27
comment Find the pair of values $a[i]$, $a[j]$ such that $a[i]\,\&\,a[j]$ is maximum
@900sit-upsaday: Thanks, I have cast my dupe vote there.
Jul
27
comment Find the pair of values $a[i]$, $a[j]$ such that $a[i]\,\&\,a[j]$ is maximum
You haven't clarified the bitwise AND part (this is a mathematics site :-)). Also, as written, the question gives the impression that you haven't put any effort into it, which clearly isn't true. Why not edit the question and put in some motivation and your ideas and requirement of a linearithmic algorithm, and turn this into good question (according to the standards of this site)?
Jul
27
comment Find the pair of values $a[i]$, $a[j]$ such that $a[i]\,\&\,a[j]$ is maximum
$a[i] \& a[j]$ is bitwise AND of $a[i]$ and $a[j]$? Where did you come across this problem? What is wrong with the trivial $\Theta(n^2)$ brute force algorithm? Is this a puzzle you are posing here?
Jul
25
comment Asymptotic Behaviour Of A Bizarre Function 2
Related: math.stackexchange.com/questions/115824/…
Jul
25
comment Asymptotic Behaviour Of A Bizarre Function 2
@900sit-upsaday: Thanks! Wasn't aware of this nice feature. Been away from stackexchange long enough...
Jul
24
comment How prove this $\sum_{cyc}\frac{x+y-2z}{(x+y)^2+z^2}=0$
Why is this tagged inequality?
Jul
24
comment Polynomial representation
@Minu: Yes, that is correct.
Jul
24
comment Polynomial representation
@Mathmo123: Don't know. Let's see Minu's response. (You might be right though)
Jul
24
comment Prove that an expression is zero for all sets of distinct $a_1, \dotsc, a_n\in\mathbb{C}$
@DamianPavlyshyn: Yes, or more simply, replace $a_1$ by $z$, do some algebra to get a polynomial in $z$ which has infinite roots (any $z \ne a_i$), allowing setting $z=0$.
Jul
23
comment Prove that an expression is zero for all sets of distinct $a_1, \dotsc, a_n\in\mathbb{C}$
Look at the Lagrange polynomial of $P(a_i) = a_i$
Jul
19
comment Proving that one of $a(1-b), b(1-c), c(1-a) \le \frac{1}{4}$
For $a,b,c \le 1$, see my comment to DanZimm. There is no need of $c$ if $a \le b$. There is an implicity renaming of variables going on. For instance if you chose $a=0.3, b = 0.1, c = 0.4$, we kind of have implicitly swapped $b$ and $c$ in our proof...
Jul
19
comment Proving that one of $a(1-b), b(1-c), c(1-a) \le \frac{1}{4}$
@DanZimm: If $c \ge 1$, then $b(1-c) \le 0$.
Jul
19
comment Always null recurrence at the boundary between positive recurrence and transience?
Can you think of a better title?
Jul
18
comment Solving the integral $\int_{0}^{\infty} \frac{\sin{x}}{x} \ dx = \frac{\pi}{2}$?
@V-Moy: I am flattered! Glad that my answers have been helpful. :-)
Jul
18
comment Solving the integral $\int_{0}^{\infty} \frac{\sin{x}}{x} \ dx = \frac{\pi}{2}$?
@V-Moy: Thank you for your kind comments! (and the badge :-))
Jul
18
comment What is the integral of x/ln(x)?
See: en.wikipedia.org/wiki/Exponential_integral