Show that a next polynomial function sequence converges uniformly to $\sqrt{x}$
48792
Prove $p_n(x) \rightarrow \sqrt{x}$ uniformly as $n \rightarrow \infty$
38752
Uniform convergence of $\sum (-1)^nf_n(x)$ on $[0,1]$ where $f_n(x)=x^n(1-x)$.
148410
How do I show $f_n(x)=n^2 x^n(1-x)$ pointwise converges to $0$ on $[0,1]$?
111475
Uniform convergence and the supremum theorem
118362
Determine whether $f_n(x)=\frac{x^n}{\sqrt{3n}}$ for $x \in [0,1]$ is uniformly convergent
149055
Uniform convergence of $\sum\limits_{k=1}^{\infty}\dfrac{kf(x^2)}{1+k^3f(x^2)^2}$
16228
Show that there is sequence of homeomorphism polynomials on [0,1] that converge uniformly to homeomorphism
141484
Convergence of a sequence by convergence of sub-subsequence
124382
Showing that $f_n:[0,1]\to\mathbb{R}$ when $f_n=nx(1-x)^n$ converges pointwise but not uniformly
79451
Uniform convergence on two separate intervals
147764
show that $f(z)+f(z^2)+\cdots + f(z^n)+\cdots$ converges locally uniformly to an analytic function in the unit disk.
65312
Check the uniform convergence of series of functions
18153
To prove that $f_n(x) = \frac{nx}{1+n^2x^2}$ does not uniformly converge to $f(x) = 0$ on $[0,1]$
107399
A sequence and convergence
49828
Show that the sequence $\sqrt{2},\sqrt{2\sqrt{2}},\sqrt{2\sqrt{2\sqrt{2}}},...$ converges and find its limit.
106000
Determine if $f_n(x)= \big(\cos (\frac x {\sqrt n} )\big )^n $ converges pointwise or/and uniformly?
93022
Prove that a given recursion sequence converges