query: elementary Uniform convergence question
positive_passages.docid: 18153
positive_passages.text: To prove that $f_n(x) = \frac{nx}{1+n^2x^2}$ does not uniformly converge to $f(x) = 0$ on $[0,1]$
negative_passages.docid: 63612
negative_passages.text: Determine convergence of $\sum_{n=1}^{\infty}a_n$
negative_passages.docid: 144530
negative_passages.text: is uniform convergent sequence leads to bounded function?
negative_passages.docid: 155695
negative_passages.text: The convergence of a sequence
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: 37389
negative_passages.text: Why is this sequence of functions not uniformly convergent?
negative_passages.docid: 107399
negative_passages.text: A sequence and convergence
negative_passages.docid: 55826
negative_passages.text: Convergence of sequence of real numbers and (sub)subsequence
negative_passages.docid: 133198
negative_passages.text: Show that $(1+\frac{x}{n})^n e^{-x} \rightarrow 1$ converges uniformly.
negative_passages.docid: 85217
negative_passages.text: Boundedness and convergence of $x_{n+1} = x_n ^2-x_n +1$
negative_passages.docid: 4834
negative_passages.text: Proving that unconditional convergence is equivalent to absolute convergence
negative_passages.docid: 114315
negative_passages.text: The sequence 1/(n-1) is apparently unbounded yet convergent. What am I missing here?
negative_passages.docid: 142645
negative_passages.text: $f_n$ converges uniformly on $[a,b]$ to some function $f$
negative_passages.docid: 102076
negative_passages.text: Sequence of monotone functions converging to a continuous limit, is the convergence uniform?
negative_passages.docid: 135110
negative_passages.text: Pointwise convergence of $h_n(x) = x^{1+\frac{1}{2n-1}}$
negative_passages.docid: 65312
negative_passages.text: Check the uniform convergence of series of functions
negative_passages.docid: 20287
negative_passages.text: Convergence Problem.