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 Jan 20 awarded Popular Question Jul 2 awarded Curious Aug 18 awarded Good Question Mar 12 awarded Yearling Jun 8 awarded Constituent Jun 8 awarded Caucus Mar 12 awarded Yearling Jul 31 comment Sum with sine in denominator +1 -- Nice answer, indeed! :] Jul 31 comment Is $\int \frac{7-x}{x^3-x^2-x-2}dx$ solvable using elementary functions? Is it solvable at all? @J.M. Thanks. I've always wondered what the root-sum thingy meant. Jul 10 answered Need help in Taylor series expansion Jul 3 comment Summation formula name If, to find $S_{p} = \sum_{k=1}^{n}k^p$, it requires that we know $S_{1}, \ldots, S_{p-1}$, then it isn't that effective, surely? I can think of an extremely simple way to do that -- or, at least, when p is odd! Jul 3 comment Proof that $\sum\limits_{k=1}^nk^2 = \frac{n(n+1)(2n+1)}{6}$? +1. I'm in love with this one! Jun 18 revised Necessary and sufficient condition for the coefficients of a quartic deleted 76 characters in body Jun 18 comment Necessary and sufficient condition for the coefficients of a quartic Sorry about the typos/mistakes in the main body of this problem. I've an exam in few days so I sort of panicked when I couldn't do this one. Jun 18 comment Necessary and sufficient condition for the coefficients of a quartic @Ross Millikan - Thank you. So for the second part, the following suffices... \begin{aligned} & \frac{(2v)(2w+v^2)}{2}-\frac{1}{8}(2v)^3 \\& = \frac{8v(2w+v^2)-8v^3}{8} \\& = \frac{16vw+8v^3-8v^3}{8} \\& = \frac{16vw}{8} \\& = 2vw.\end{aligned} ... as it satisfies our necessary and sufficient condition, and hence the 'if and if only if'. Jun 18 revised Necessary and sufficient condition for the coefficients of a quartic deleted 2 characters in body Jun 18 comment Why do we take a derivative? +1. This explanation makes me smile! :] Jun 18 revised Necessary and sufficient condition for the coefficients of a quartic added 14 characters in body Jun 18 comment Necessary and sufficient condition for the coefficients of a quartic @Ross Millikan, Okay, I think I get the problem now. So if I take $a = 2, b = 3, c = 2$ -- then I get $r = 1$. Also $2 = p+2s$ and $2 = p+2s$. Writing $s = 1-p/2$, we take any value of $p$, say, $p = 4$; then we have $s = -1$ and since $s²+q+ps = 0$, we have $q = 3$. Jun 18 revised Necessary and sufficient condition for the coefficients of a quartic edited body