query: How to prove that $f_n(x)=\frac{nx}{1+n\sin(x)}$ does not converge uniformly on $[0, \pi/2]$?
positive_passages.docid: 26291
positive_passages.text: Does $\frac{nx}{1+n \sin(x)}$ converge uniformly on $[a,\pi/2]$ for all $a \in (0,\pi/2]$?
negative_passages.docid: 126656
negative_passages.text: Convergence or divergence of $\sum\limits_n(-1)^{\pi(n)}\frac1n$ where $\pi(n)$ is the number of primes less than or equal to $n$
negative_passages.docid: 133874
negative_passages.text: Proof that $\lim_{n\to\infty}{\sin{100n}}$ does not exist
negative_passages.docid: 6345
negative_passages.text: Is the $\sum\sin(n)/n$ convergent or divergent?
negative_passages.docid: 37389
negative_passages.text: Why is this sequence of functions not uniformly convergent?
negative_passages.docid: 100574
negative_passages.text: Convergence of $\sum_n \frac{n!}{n^n}$
negative_passages.docid: 157422
negative_passages.text: Why $\sin(nx)$ converges weakly in $L^2(-\pi,\pi)$?
negative_passages.docid: 150305
negative_passages.text: $f_{n+1}(x):= \int_a ^x f_n(t)dt$, $\sum_{m=1} ^{\infty} f_m(x)$ is uniformly convergent
negative_passages.docid: 14031
negative_passages.text: Why does the series $\sum_{n=1}^\infty\frac1n$ not converge?
negative_passages.docid: 54202
negative_passages.text: Show that the series $\sum(\exp(\frac{(-1)^n}{n})-1)$converges, but not absolutely.
negative_passages.docid: 85092
negative_passages.text: Proving $ f(x) = x^2 $ is not uniformly continuous on the real line
negative_passages.docid: 149360
negative_passages.text: convergence of $ \sum_{k=1}^\infty \sin^2(\frac 1 k)$
negative_passages.docid: 133198
negative_passages.text: Show that $(1+\frac{x}{n})^n e^{-x} \rightarrow 1$ converges uniformly.
negative_passages.docid: 63418
negative_passages.text: Show that $f_n(x) = \frac{x^2}{n}$ for $x \in \mathbb{R}$ does not converge uniformly towards $0$ for $n \rightarrow \infty$
negative_passages.docid: 125925
negative_passages.text: Convergence of $f_n(x)=x^n(1-x)^n$
negative_passages.docid: 25532
negative_passages.text: Determine if the convergence of $f_n(x) = \sqrt{x^2 + \frac{1}{n^2}}$ is uniform.
negative_passages.docid: 16480
negative_passages.text: Does $\sum_{n=1}^{\infty}\ln(n\sin(\frac{1}{n}))$ converge?