Why is $(f_n)_{n\in\mathbb{N}}$ with $f_n :[0,1]\rightarrow\mathbb{R}, f_n(x)=x^n$ not uniformly convergent?
135450
Prove $x^n$ is not uniformly convergent
142645
$f_n$ converges uniformly on $[a,b]$ to some function $f$
46323
Criteria for convergent sequence (Baby Rudin Theorem 3.22)
30167
Convergence of $\sqrt[n]{x^n+y^n}$ (for $x, y > 0$)
156905
Prove $f_n$ has a uniformly convergent subsequence on $[0,1]$.
85217
Boundedness and convergence of $x_{n+1} = x_n ^2-x_n +1$
155822
Does uniform convergence preserves absolute continuity?
84969
When does $\lim_{n\rightarrow \infty} a_n = 0$ imply $\sum_{n = 0}^{\infty} a_n$ converges?
129087
Proof that a sequence of continuous functions $(f_n)$ cannot converge pointwise to $1_\mathbb{Q}$ on $[0,1]$
41482
$f_n → f$ uniformly on $S$ and each $f_n$ is cont on $S$. Let $(x_n)$ be a sequence of points in $S$ converging to $x \in S$. Then $f_n(x_n) → f(x)$.
35535
Sequence of sets $f_n$ that converge almost everywhere to $f$ but not almost uniformly to $f$?
54659
How prove that $(a_{n})_{n \in \mathbb{N}}$ is convergent with $a_{0}=1$, $a_{n+1}= \sqrt{2a_{n}}$?
83040
Proving that the sequence $F_{n}(x)=\sum\limits_{k=1}^{n} \frac{\sin{kx}}{k}$ is boundedly convergent on $\mathbb{R}$
127251
$f_n(x) = \cos \left( \sqrt{x^2 + \frac{1}{n} }\right)$ is uniformly convergent
137997
Does the series $\sum \frac{x^n}{1+x^n}$ converge uniformly on $x\in [0,1)$?
138397
If a sequence of functions $f_n$ converges uniformly to $f$, does this imply $f_n$ is continuous? How to prove?
114702
$\int_0^{\infty} f(x)dx$ converges and $\lim_{x\rightarrow \infty} f(x)$ exists, then $\lim_{x\rightarrow \infty} f(x)=0$?