query: Is $f\left(x\right)=nx^{n}\left(1-x\right)$ uniformly convergent on $x\in\left[0,\:1\right]$
positive_passages.docid: 153063
positive_passages.text: Uniform convergence of $f_n(x)=nx^n(1-x)$ for $x \in [0,1]$?
negative_passages.docid: 8913
negative_passages.text: Show that there is $\xi$ s.t. $f(\xi)=f\left(\xi+\frac{1}{n}\right)$
negative_passages.docid: 110680
negative_passages.text: Convergence of recursive sequence $a_{n+1} =\frac{ 1}{k} \left(a_{n} + \frac{k}{a_{n}}\right)$
negative_passages.docid: 135450
negative_passages.text: Prove $x^n$ is not uniformly convergent
negative_passages.docid: 43576
negative_passages.text: Convergence of $\sum _{n=1}^{\infty }\left\{ 1-n\log \frac {2n+1} {2n-1}\right\} $
negative_passages.docid: 138516
negative_passages.text: $\sum (-1)^{n+1}\log\left(1+\frac{1}{n}\right)$ convergent but not absolutely convergent
negative_passages.docid: 76756
negative_passages.text: A convergence proof: $\lim_{n\to\infty} \left(1+n^2\right)^{\frac1n}$
negative_passages.docid: 35547
negative_passages.text: Does $\{f_ng_n\}\to fg$ uniformly?
negative_passages.docid: 142928
negative_passages.text: Proving $\left\{ \frac{1}{n} \right\}$ is Cauchy
negative_passages.docid: 6815
negative_passages.text: $\lim_{n \rightarrow\infty} ~ x_{n+1} - x_n= c , c > 0$ . Then, is $\{x_n/n\}$ convergent?
negative_passages.docid: 16228
negative_passages.text: Show that there is sequence of homeomorphism polynomials on [0,1] that converge uniformly to homeomorphism
negative_passages.docid: 94910
negative_passages.text: How does one show that $\lim_{x\rightarrow\infty}\left(1+\frac{1}{x}\right)^x$ converges?
negative_passages.docid: 67303
negative_passages.text: If $\sum_{n=2}^{\infty} a_n$ is convergent, is $\sum_{n=2}^{\infty}{\sqrt{a_n} \over \ln{n}}\left( n^{a_n}-1 \right)$ convergent as well?
negative_passages.docid: 62937
negative_passages.text: Test for the convergence of the sequence $S_n =\frac1n \left(1 + \frac{1}{2} + \frac{1}{3} + \cdots+ \frac{1}{n}\right)$
negative_passages.docid: 95515
negative_passages.text: Is $x_{n+1}=\cos x_n$ convergent?
negative_passages.docid: 133707
negative_passages.text: Notions of strong and weak convergence for $L^{2}(\mathbb R, \lambda)$ where $f_{n}(x)=1_{[n,n+1]}(x)$
negative_passages.docid: 156141
negative_passages.text: Limit of $\left(1-\frac{1}{n^2}\right)^n$