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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
Jun
18
comment Necessary and sufficient condition for the coefficients of a quartic
You're right, fixed that too!