Prove that $\sin(n\pi x)$ weakly converges to $0$ in $L^2(0,1)$
138086
Can we prove the Riemann-Lebesgue lemma by using the Weierstrass approximation theorem?
140901
Uniform convergence of $f_n(z)=nz^n$ in the set $|z|<\frac{1}{2}$
41862
Asymptotic behavior of a trigonometric series
82567
Prove that $ f(x) $ has at least two real roots in $ (0,\pi) $
129087
Proof that a sequence of continuous functions $(f_n)$ cannot converge pointwise to $1_\mathbb{Q}$ on $[0,1]$
119317
Proving the series of partial sums of $\sin (in)$ is bounded?
118687
Prove an inequality with a $\sin$ function: $\sin(x) > \frac2\pi x$ for $0<x<\frac\pi2$
45728
Proving a limit of a trigonometric function: $\lim_{x \to 2/\pi}\lfloor \sin \frac{1}{x} \rfloor=0$
60217
Proof: Series converges $\implies $ the limit of the sequence is zero
117264
Prove that $\int_0^{\infty} \frac{\sin x}{x^p}\, dx$ converges for $0<p<2$
9244
Does the sequence $\{\sin^n(n)\}$ converge?
139113
Does the series $\sum \sin^{(n)}(1)$ converge, where $\sin^{(n)}$ denotes the $n$-fold composition of $\sin$?
60891
Does $\sum\limits_{k=1}^\infty |\sin(ak)/k|$ converge?
72606
Prove that : $a_n>0$, Then, $\sum_{n=1}^\infty a_n$ converges iff $\sum_{n=1}^\infty \sin(a_n)$ converges.
133707
Notions of strong and weak convergence for $L^{2}(\mathbb R, \lambda)$ where $f_{n}(x)=1_{[n,n+1]}(x)$
85388
Prove that the limit of $\sin n$ as $n \rightarrow \infty$ does not exist
148410
How do I show $f_n(x)=n^2 x^n(1-x)$ pointwise converges to $0$ on $[0,1]$?