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 Apr 30 comment Prove that $(a_n) \in l_2$. Do you know the Riesz representation theorem? Apr 29 revised How $1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+\cdots =\ln 2$? edited title Apr 28 answered Given $\int _{-1}^{1}g(x)= 1$ show that $\int _{-1}^{1}f(x)g(x)\geq 1$ for certain $f,g$. Apr 28 comment $\{(1), (12)(34), (13)(24), (14)(23)\}$ is the only non-cyclic proper subgroup of $A_4$? If you show the above is the unique normal subgroup of order 4, then I think you are done. Apr 28 awarded Popular Question Apr 19 answered Solving $\cos(t)y' + y\sin(t) = \cos^4(t)$? Apr 1 asked Fourier series method of solving inhomogenous wave equation on infinite interval? Mar 26 revised Why does adding a term $5f'(t)$ to $5f''(t)+10f(t)=0$ cause damping? edited title Mar 24 comment Fourier transform of $\|x\|^{-n}$ in $\mathbb R^n$ with cut-off at $0$ This is equivalent to computing $\int_c^\infty \sin(x)/x dx$ after changing to spherical coordinates. Mar 21 comment Resolution of equation such that $f(…f(x)…)=x$ Sorry, I actually think partition numbers come into play. Mar 21 comment Resolution of equation such that $f(…f(x)…)=x$ Well, for composite $n$ you can construct factor solutions. Maybe if those are all the solutions for $n$ you can restate the problem as finding solutions for $f^{(p)}(x)=x$, $p$ prime. Mar 21 comment Eigenvalues of a matrix with a concentric arrangement of coefficients Doing Gaussian elimination to get an upper triangular matrix. I.e., an $LU$ decomposition, you'll get diagonal entries of $U$ as $d_1, d_2-d_1, d_3-d_2-d_1, \dots, d_n-d_{n-1}-\cdots-d_1$. Maybe there is a hint here of some diagonalization process? Mar 20 answered Show $Px \perp (x-Px)$ and prove $||P|| \leq 1$ Mar 17 comment Show that $H_{2^n}$ $\leq$ $1+n$ with induction Do you know the famous proof of the divergence of the harmonic series? Mar 17 comment Integrating, the $\int_0^\infty \frac{\text{ d}x}{x^2\ln x+1}$ Looks like a candidate for contour integration. Mar 14 answered Finding roots of $\sin(x)=\sin(ax)$ without resorting to complex analysis Mar 10 comment Why define norm in $L_p$ in that way? What!? No mention of Cauchy Schwarz or Holder on this question? Mar 10 awarded Pundit Mar 8 comment Proof that $T: l^2 \rightarrow l^2$ is compact with $T(x) = \left(\frac{x_1}{1},\frac{x_2}{2},\dots\right)$ Continuous functions always map compact sets to compact sets. What it means for $T$ to be a compact operator is that any bounded set is mapped to a relatively compact set--i.e. a set whose closure is compact. Mar 7 revised In which $L^p$-Space is the following function? deleted 11 characters in body; edited tags