query: Is $j_n(x)=\frac{x}{1+n^2x^2}$ uniformly convergent on $[0,1]$?
positive_passages.docid: 157762
positive_passages.text: Showing $f_n(x):=\frac{x}{1+n^2x^2}$ uniformly convergent in $\mathbb R$ using $\epsilon-n_0$
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: 9263
negative_passages.text: Convergence of $\sum_{n=1}^\infty\frac{n!\, i^n}{n^n}$
negative_passages.docid: 32042
negative_passages.text: Convergence of $\sum_{n=1}^\infty \frac{n^2}{2^n}$
negative_passages.docid: 143642
negative_passages.text: Does the sequence $(\sqrt{n} \cdot 1_{[0, 1/n]})_n$ converge weakly in $L^2$?
negative_passages.docid: 9244
negative_passages.text: Does the sequence $\{\sin^n(n)\}$ converge?
negative_passages.docid: 100574
negative_passages.text: Convergence of $\sum_n \frac{n!}{n^n}$
negative_passages.docid: 22450
negative_passages.text: Convergence of $\sum\limits_{n=2}^\infty \frac{1}{n^\alpha \ln^\beta (n)} $ for nonnegative $\alpha$ and $\beta$
negative_passages.docid: 26291
negative_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: 59260
negative_passages.text: How to prove the convergence of $\sum_{n\geq 0}\frac{n!^d}{(dn)!}$ for $d\geq 2$?
negative_passages.docid: 94868
negative_passages.text: When does $P(x)=\sum_{n=0}^{\infty}{\frac{n!}{n^n}\cdot x^n}$ with $x\in \mathbb{C}$ converge?
negative_passages.docid: 68081
negative_passages.text: x/n uniformly convergent?
negative_passages.docid: 70867
negative_passages.text: Is $\sum_{n=1}^\infty\frac{(-1)^n}{n\log^2(n+1)}$ absolutely convergent?
negative_passages.docid: 44288
negative_passages.text: Is my proof of convergence for $\sum\limits^{\infty}_{n=1} \frac {2^n} {n^n}$ true?
negative_passages.docid: 29751
negative_passages.text: Dini's Theorem and tests for uniform convergence
negative_passages.docid: 23969
negative_passages.text: Why isn't $nxe^{-nx}$ uniformly convergent for $x \geq 0$?
negative_passages.docid: 146024
negative_passages.text: Help with counter-example on uniformly convergence.