Show that there exists a sequence $\phi_n \in C_c^{\infty}(\mathbb{R}^n)$ such that $\lim_{n \to \infty}||\phi_n - f||_p = 0$
53173
Infinitely differentiable functions with compact support are dense in $L^p$
70590
limit of a sequence. might be related to Cesaro theorem
46065
How do you find all $n$ such that $\phi(n)|n$
144786
Show that the following inductively defined sequence converges and find its limit.
155695
The convergence of a sequence
39488
Limit of a sequence involving root of a factorial: $\lim_{n \to \infty} \frac{n}{ \sqrt [n]{n!}}$
7815
Prove that $\lim_{n\to\infty}a_n^2=a^2$ when ${a_n}$ is a sequence in $\mathbb{R}$ with $\lim_{n\to\infty}a_n=a$
124844
Show that $\phi \circ f$ belongs to $L_p$ for each $f \in L_p$
99117
Existence of a sequence of positive continuous functions on $\mathbb R$ which is unbounded precisely on $\mathbb Q$
92447
About the $p$ summable sequences
41057
Does $L^p$-convergence imply pointwise convergence for $C_0^\infty$ functions?
100580
Proof that a sequence converges.
63608
Cauchy sequence in a normed space
1760
Limit of the geometric sequence $\{r^n\}$, with $|r| < 1$, is $0$?
71350
Let $H$ be a Hilbert space with projections $P,Q$, then $\lim_{n\to\infty}(PQ)^nx= Rx$ for all $x\in H$, where $R$ is the projection to $PH\cap QH$
31836
Proof of $\lim_{n\to \infty} \sqrt[n]{n}=1$
137446
Show that if $b_k\uparrow \infty$ and $\Sigma_{k = 1}^\infty a_kb_k$ converges, then $b_m \Sigma_{k = m}^\infty a_k → 0$ as $m → \infty$.