Aryabhata
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 Jan 22 comment Proving that a sequence is bounded without knowing the sequence explicitly What is the starting value? Jan 6 comment Computing limits which involve square roots, such as $\sqrt{n^2+n}-n$ @Normal: I suggest you read this: meta.math.stackexchange.com/questions/1868/… and the linked question by Bill D. Special case vs general case is a common objection to such closings, but such closings [i.e. closed as minor variations] are fine IMO. It does not have to be an exact dupe. Jan 4 comment Computing limits which involve square roots, such as $\sqrt{n^2+n}-n$ Please consider browsing the faq tag before posting a question. [To anyone who comes across this comment, I know this question is old] Jan 4 comment Computing limits which involve square roots, such as $\sqrt{n^2+n}-n$ Dec 18 comment Is $a^{\ln b} = b^{\ln a}$? Take log on both sides and compare. Dec 18 comment Lottery Math (different combinations) Dec 7 comment Proving the positivity of a twice-differentiable real-valued function @Eklavya: Intermediate value theorem. Nov 25 comment Existence of a self-complementary graph @SalmonKiller: I have added more explanation... Nov 21 comment Proof that $\lim_{n\rightarrow \infty} \sqrt[n]{n}=1$ @GniruT: Thanks! Glad you liked it. Oct 26 comment Determine angle $x$ using only elementary geometry @user236182: You are right. Oct 2 comment The Modified Faro shuffle. This site has latex support via mathjax: meta.math.stackexchange.com/questions/5020/… Oct 2 comment Why a shuffling algorithm is not uniformly random between [1, N)? Yeah, I use it. Bridge! (Thank you for that....) Oct 2 comment Why a shuffling algorithm is not uniformly random between [1, N)? +1: Nice way to look at it. Sep 14 comment Estimating $\sum n^{-1/2}$ @achillehui: Euler Mc Laurin Summation gives that, and more (except for $\zeta(1/2)$). Sep 11 comment Moebius function log sum Are you asking for a proof of that? Where did you find that identity? Sep 10 comment Recognizable vs Decidable @EricLeschinski: I am not sure what you are trying to say. We are talking about Turing machines. Talking about programming languages seems irrelevant. Sep 9 comment How can you prove that a function has no closed form integral? @Mauris: Thanks. Jul 19 comment Solving recurrence $T(n) = T(\lceil n/2 \rceil) + T(\lfloor n/2 \rfloor) + \Theta(n)$ @IntrepidTraveller: We are considering a mathematical recurrence, it could be space/time complexity or even something else (like number of comparisons). Besides, we can replace $T$ in the above post with $G$ where $G(n) = T(n) - T(1)$ and for that $G$, $G(1)$ is indeed $0$. $T(1) = 0$ is taken to simplify the math, and does not change the end result. Jun 9 comment How do I solve inequalities of the form $\left|\frac{f(x)}{g(x)}\right| \geq 1$? @StevenGregory: You can. Notice the absolute values... Jun 9 comment If $A,B,C,D$ are complex numbers on the unit circle with $A+B+C+D=0$, then they form a rectangle @YotasTrejos: It is not a square. Basically, given $A$, you just reflect it along x and y axis, and then take the negative to get the four corners of the quadrilateral. Now take $A$ close to the y axis and far far away from the x axis. Do you still get a square?