Reputation
21,913
Next tag badge:
93/100 score
30/20 answers
Badges
2 25 43
Newest
 Informed
Impact
~213k people reached

Feb
3
answered Is it true that GCD$(\alpha,b)=1$?
Jan
31
awarded  Good Answer
Jan
28
comment analytic solution of a definite integral
Surely, this cries out for subsituting $u=(1+x^c)^k-1$, does it not?
Jan
28
comment analytic solution of a definite integral
Under no circumstance use asterisks for multiplication (except in computer programming, where you don't have any other choice, of course). In mathematics, it most commonly denotes convolution, which is another type of beast entirely. If you need a multiplication sign, use \cdot ($\cdot$) instead.
Jan
27
comment Is every shape possible with a snake?
@Lembik I see. That's good.
Jan
27
comment Is every shape possible with a snake?
@Lembik I don't mind. But it is common to give credit when you use other people's work this way, say by linking here. I don't really care if you do in this case, but if it were the result of a bigger effort, I might care. So to play it safe, you should get into the habit of providing that link.
Jan
27
comment Is every shape possible with a snake?
@Lembik If it does, then the head will touch the adjacent bit of snake, right? I had assumed this was disallowed. If it is allowed, then you're right, but that is the only thing you can do. Of course, if a 180° turn is allowed, so a length of snake is on top of the adjacent length, then any shape is trivially reachable, since the snake can just roll itself up into a single segment and the unroll itself into the required shape.
Jan
27
comment Is every shape possible with a snake?
@hardmath Ah well, I fixed it with some unicode box art. Unfortunately, there is a small gap between the text lines which makes breaks in the vertical lines, but it can't be helped.
Jan
27
revised Is every shape possible with a snake?
ASCII to unicode
Jan
27
comment Is every shape possible with a snake?
@hardmath Indeed. If I had deleted the four seemingly redundant text lines, I would end up with an ambiguous looking stack of three pluses on the right margin. I could probably have done better if I looked up the line art characters that exist somewhere in unicode land, though.
Jan
27
answered Is every shape possible with a snake?
Jan
26
comment Prove that $2^{3^n} + 1$ is divisible by 9, for $n\ge1$
I fixed the formatting for you. But please, please, do provide some context and tell us what you tried.
Jan
26
revised Prove that $2^{3^n} + 1$ is divisible by 9, for $n\ge1$
Fixed latex problem, language and tagging
Jan
26
comment Prove the following.
Did you try isolating $\sqrt{a-1}$ on one side of the desired inequality, and then squaring? (You do, of course, need to be a little careful when squaring an inequality …)
Jan
26
comment Convergence of $\sum_{n=1}^{\infty} \log~ ( n ~\sin \frac {1 }{ n })$
Minor nit: Where you write (error $\ll\frac1{x^4}$), the $\ll$ is a bit too strong.
Jan
25
answered Convergence of $\sum_{n=1}^{\infty} \log~ ( n ~\sin \frac {1 }{ n })$
Jan
25
comment Convergence of $\sum_{n=1}^{\infty} \log~ ( n ~\sin \frac {1 }{ n })$
You used the inequality $\log x<x$, which is way too weak to be of use. When $x\approx1$, $\log x\approx0$ after all. Question: Do you know the Taylor series for $\sin x$?
Jan
25
comment Prove that if $\left({x+\sqrt{x^2+1}}\right)\left({y+\sqrt{y^2+1}}\right)=1$ then $x+y=0$
From a superficial reading, I'll say your proof looks OK. Why does it surprise you that very different proofs might exist?
Jan
24
comment get a integral from another
@AndréNicolas I realized this too, just after writing my former comment. But then this is a bit of a trick question, in that it encourages you to try writing one integral in terms of the other instead of just evaluating each on its own. Nasty.
Jan
24
comment get a integral from another
@user208259 I imagine the answer is desired in terms of $A$, not $\alpha$. The latter is easy following your suggestion. The former, not so much.