Aryabhata

47,595 reputation

379168

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Don't have much time these days...

	47,595 reputation	bio	website		visits	member for	2 years, 9 months
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Sep 27	comment	Recurrence relation for $a_{n}$ where $6a_{n}$ and $10a_{n}$ are both triangular What exactly do you mean by characterize? Is the recurrence relation given in your link to A180926 not sufficient?
Sep 27	comment	Find the sum to n terms of the series $\displaystyle \frac{1} {1.2.3.4} + \frac{1} {2.3.4.5} + \frac{1} {3.4.5.6} $ @Branimir: You are welcome! And I see you joined today, welcome to this site :-)
Sep 27	awarded	Civic Duty
Sep 27	comment	Find the sum to n terms of the series $\displaystyle \frac{1} {1.2.3.4} + \frac{1} {2.3.4.5} + \frac{1} {3.4.5.6} $ +1: Even though the question says first n terms, this can easily be adapted for that.
Sep 27	answered	$k^{2}+(k+1)^{2}$ being a perfect square for infinitely many $k$
Sep 26	comment	How to build a linear equation system? Are you trying to create test cases for your linear equation solver? If so, you could just generate the equations randomly and then verify the solution given by your solver by substitution into the original equations.
Sep 25	comment	How do I solve inequalities of the form $\left\|\frac{f(x)}{g(x)}\right\| \geq 1$? @mweerden: Well it amounts to finding the points where h(x) = (f(x)+g(x))(f(x)-g(x)) is non-negative. In case f(x) and g(x) are linear, this can easily be done without pen and paper! In some sense, there are fewer cases to consider here.
Sep 25	answered	Is there possibly a largest prime number?
Sep 25	comment	How is this series in denominator converted to a series in numerator? @Harpreet: No worries! btw, Welcome to this site. I hope you will find it useful.
Sep 25	comment	How is this series in denominator converted to a series in numerator? @Mariano: I was expecting the OP will do it himself... Anyway, I went ahead and made the change.
Sep 25	revised	How is this series in denominator converted to a series in numerator? math formatting
Sep 25	comment	How is this series in denominator converted to a series in numerator? @Harpreet: Use the dollar signs and latex between them. Example $x^2+y^2=z^2$ looks like $x^2+y^2=z^2$
Sep 25	revised	Formally proving that a function is $O(x^n)$ added condition that a > 0
Sep 25	comment	How is this series in denominator converted to a series in numerator? @Isaac: I interpreted it the same way too and added an answer with that interpretation.
Sep 25	answered	How is this series in denominator converted to a series in numerator?
Sep 25	answered	How do I solve inequalities of the form $\left\|\frac{f(x)}{g(x)}\right\| \geq 1$?
Sep 25	comment	Formally proving that a function is $O(x^n)$ @alex: Yeah, since this seems like homework, just trying to make sure Joel knows the right definition taught in their class :-)
Sep 25	revised	Formally proving that a function is $O(x^n)$ fixed title.
Sep 25	comment	Lateral surface area of a region Was an exact answer expected? Or a numerical approximation was enough?
Sep 25	comment	Formally proving that a function is $O(x^n)$ If $a < 0$, then the $0 \le kg(x)$ is violated... Perhaps a different definition? Or can $k < 0$?