# Tagged Questions

For questions about uniform convergence of a sequence or a series of functions on a set. Also used with the tag [convergence].

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### Checking if $(x^{2n}-1.5x^n+\frac12)^\infty_{n=1}$ converges uniformly on$[\frac12,1]$ and on $[0,\frac12]$

Checking if $\left(x^{2n}-1.5x^n+\frac12\right)^\infty_{n=1}$ on $[\frac12,1]$ and on $[0,\frac12]$. What tests/techniques do I use to prove uniform convergence?
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### Test the uniform convergence of $x^n-x^{2n}$ in $[0,1]$

$$f_n(x)=x^n-x^{2n} \\ f_n:[0,1]\rightarrow \mathbb R$$ I know that the function $x^n$ is not converging uniformally because the limiting function is not continuous (when x=1 there's a "step" in ...
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### Prove the uniform convergence of $f_{1}(x)= \sqrt x , f_{n+1}(x)=\sqrt{x+f_n(x)}$ in $[0,\infty]$

As far as I understand most of these questions use the M-test, but I can't find a series that suffices.
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### Uniform convergence of $(1 − x^{n+1})/(1 − x)$ [closed]

Prove that the sequence $(1 − x^{n+1})/(1 − x)$ converges uniformly to $1/(1 − x)$ on each interval of the form $[−r, r]$ with $r < 1,$ but it does not converge uniformly on $(−1, 1).$
Let G be a simply connected domain, $G \not \neq \mathbb{C}$ and $z_0 \in G$, I got to show that for every $n \in \mathbb{N}$ there is a holomorphic and injective mapping: $f_n:G \rightarrow D_1(0)$, ...