David Mitra
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 19h comment Express $\sec(2x)$ and $\tan(2x)$ in terms of $\tan x$ $\tan^2 x+1=\sec^2 x$. 1d reviewed Approve How to get sine / cosine value out of tangens 2d comment If $\{a_k\} \in \ell^2$, how to prove $\sum a_k/k$ converges absolutely. You're welcome. 2d comment If $\{a_k\} \in \ell^2$, how to prove $\sum a_k/k$ converges absolutely. Take $b_n=1/n$. Then from the above $|a_n b_n|\le{1\over2}(a_n^2+b_n^2) ={1\over2}(a_n^2+{1\over n^2})$. Use the Comparison Test. 2d comment If $\{a_k\} \in \ell^2$, how to prove $\sum a_k/k$ converges absolutely. $0\le(a-b)^2=a^2+b^2-2ab$. 2d awarded Enlightened 2d awarded Nice Answer May 2 comment Integration of exponential and trigonometry Something very similar to this. May 2 comment Integration of exponential and trigonometry Call the integral $I$. Integrate by parts twice to obtain $I= aI+\text{stuff}$. Solve for $I$. May 2 comment Limit of the succession $\lim_{n \to{+}\infty}{n\sin(n\pi)}$ Note $\sin(n\pi)=0$ whenever $n$ is an integer. Apr 30 comment Proving/ Disproving that a set is compact in $l^2$ Each standard unit vector, $e_i$, is in $A$. Does the sequence $(e_i)$ have a convergent subsequence? Apr 30 comment Uniform Convergence on every bounded closed intervals implies Uniform Convergence on $\Bbb R$ It's not true. Take $f_n=\chi_{[-n,n]}$. This converges to the constant function $1$ uniformly on any closed, bounded interval. Apr 30 comment Convergence from another series $0\le(a-b)^2=a^2+b^2-2ab$. Apr 29 awarded Guru Apr 28 comment Continuous function rational for every point, Cantor function It's not rational at every point. Apr 28 comment Does convergence almost everywhere to an $L^p$ function and existence of a weakly convergent subsequence guarantee weak convergence? Here's one way to solve your problem. Apr 26 revised continuity of a piece wise function defined partially on a closed interval edited tags Apr 20 answered On the dimension of a real Normed Linear Space possessing a certain property Apr 20 comment Why do so many projectile motion equation examples use $-16$ as the $a$ coefficient? It's closer to $32.174$, at sea level. Apr 19 comment On the dimension of a real Normed Linear Space possessing a certain property In an infinite dimensional space $X$, take $Y$ to be the kernel of a discontinuous linear functional. This is dense in $X$ and proper; so, there is no $x\in X$ with $\text{dist}\,(x,Y)=1$.