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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
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2d
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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 $\text{dist}\,(x,Y)=1$.