Proving $f_n(x)=x^2/n$ does NOT converge uniformly to 0 for $n\rightarrow\infty$ and $x\in\mathbb{R}$
63418
Show that $f_n(x) = \frac{x^2}{n}$ for $x \in \mathbb{R}$ does not converge uniformly towards $0$ for $n \rightarrow \infty$
146024
Help with counter-example on uniformly convergence.
74145
How to prove $x^{n}$ is not uniformly continuous
112730
uniform convergence and function $\partial^k f_n(z_n) \rightarrow \partial^k f(z_0)$
7815
Prove that $\lim_{n\to\infty}a_n^2=a^2$ when ${a_n}$ is a sequence in $\mathbb{R}$ with $\lim_{n\to\infty}a_n=a$
85388
Prove that the limit of $\sin n$ as $n \rightarrow \infty$ does not exist
62892
Uniform convergence of $\sum_{n=1}^{\infty}\frac{1}{n(1+(x-n)^2)}$
55340
Prove that $r^n/n!$ converges where $n\ge r$
76593
Show that $f_n(z)=z^n$ converges locally uniformly on $|z|<1$ but not uniformly(?)
134051
Prove $x_n$ converges IFF $x_n$ is bounded and has at most one limit point
124382
Showing that $f_n:[0,1]\to\mathbb{R}$ when $f_n=nx(1-x)^n$ converges pointwise but not uniformly
37389
Why is this sequence of functions not uniformly convergent?
100234
Proving that $x^n$ converges to $0$ whenever $|x| < 1$
17048
$\sum_{n=1}^\infty\frac{z^n}{n}$ does not converge uniformly on $\mathbb{D}$.
88147
Show that $g_n(x)=nf(x+1/n)-nf(x)$ converges uniformly to $f'$
10408
Uniformly convergence of $f_{n+1}(x)= \int^x_0 f_n(t)dt$
84969
When does $\lim_{n\rightarrow \infty} a_n = 0$ imply $\sum_{n = 0}^{\infty} a_n$ converges?