query: Proving uniform convergence of $\sqrt{x^2+1/n}$
positive_passages.docid: 25532
positive_passages.text: Determine if the convergence of $f_n(x) = \sqrt{x^2 + \frac{1}{n^2}}$ is uniform.
negative_passages.docid: 87100
negative_passages.text: Decide whether $\sum_{n=1}^{\infty}(-1)^n\frac{nx}{1+n^4x^2}$ uniformly converges on $[0,\infty)$ or not
negative_passages.docid: 137997
negative_passages.text: Does the series $\sum \frac{x^n}{1+x^n}$ converge uniformly on $x\in [0,1)$?
negative_passages.docid: 54376
negative_passages.text: Convergence of the series $\sqrt[n]n-1$
negative_passages.docid: 4157
negative_passages.text: Function Sequence Uniform Convergence
negative_passages.docid: 140220
negative_passages.text: Convergence of $\sum_{n=2}^{\infty}\frac{\sqrt{a_{n}}}{\ln\, n}(n^{a_{n}}-1)$
negative_passages.docid: 27204
negative_passages.text: Proof for convergence of a given progression $a_n := n^n / n!$
negative_passages.docid: 142
negative_passages.text: Showing the sequence converges to the square root
negative_passages.docid: 156905
negative_passages.text: Prove $f_n$ has a uniformly convergent subsequence on $[0,1]$.
negative_passages.docid: 148349
negative_passages.text: Uniform convergence with two sequences of functions
negative_passages.docid: 150101
negative_passages.text: Riemann Sum of $\sqrt{x}$ with uniform partition
negative_passages.docid: 88425
negative_passages.text: Prove that $\,\sqrt [n] n < 1 + \sqrt{\frac{2}{n}}\,$
negative_passages.docid: 67638
negative_passages.text: Show that $x_{n+1}=x_n(2-ax_n)$ converges and find the limit
negative_passages.docid: 9789
negative_passages.text: Convergence of a sequence of non-negative real numbers $x_n$ given that $x_{n+1} \leq x_n + 1/n^2$.
negative_passages.docid: 49860
negative_passages.text: Determine the convergence of $\sum\limits_{n=2}^\infty \frac{\sqrt{n+1}}{n(n-1)}$
negative_passages.docid: 111475
negative_passages.text: Uniform convergence and the supremum theorem
negative_passages.docid: 32423
negative_passages.text: Convergence of $\sum _{k=1}^\infty (1-\frac{1}{k})^{k^2}$