query: Prove that $\sum_n f_n$ uniformly converges.
positive_passages.docid: 157116
positive_passages.text: Uniform convergence of alternating series
negative_passages.docid: 149055
negative_passages.text: Uniform convergence of $\sum\limits_{k=1}^{\infty}\dfrac{kf(x^2)}{1+k^3f(x^2)^2}$
negative_passages.docid: 142057
negative_passages.text: Prove that if $\sum_{n=1}^\infty a_n$ converges then $\sum_{k=1}^\infty A_k$ converges
negative_passages.docid: 76137
negative_passages.text: Too simple proof for convergence of $\sum_n a_n b_n$?
negative_passages.docid: 118362
negative_passages.text: Determine whether $f_n(x)=\frac{x^n}{\sqrt{3n}}$ for $x \in [0,1]$ is uniformly convergent
negative_passages.docid: 83040
negative_passages.text: Proving that the sequence $F_{n}(x)=\sum\limits_{k=1}^{n} \frac{\sin{kx}}{k}$ is boundedly convergent on $\mathbb{R}$
negative_passages.docid: 140901
negative_passages.text: Uniform convergence of $f_n(z)=nz^n$ in the set $|z|<\frac{1}{2}$
negative_passages.docid: 145926
negative_passages.text: To show that $\sum a_nb_n$ is absolutely convergent
negative_passages.docid: 41482
negative_passages.text: $f_n → f$ uniformly on $S$ and each $f_n$ is cont on $S$. Let $(x_n)$ be a sequence of points in $S$ converging to $x \in S$. Then $f_n(x_n) → f(x)$.
negative_passages.docid: 67006
negative_passages.text: Sequence of functions: Convergence
negative_passages.docid: 104344
negative_passages.text: Prove if $|a_{n+1}|/|a_n| \leq |b_{n+1}|/|{b_n}|$ and $\sum |b_n|$ is convergent, then $\sum |a_n|$ is convergent
negative_passages.docid: 66758
negative_passages.text: $f_n:[0,1]\to [0,1]$ continuous, $f_n\to f$ uniformly, prove: ${\frac1n}\sum_{k=1}^{n}{f_k} \to f$ uniformly
negative_passages.docid: 112730
negative_passages.text: uniform convergence and function $\partial^k f_n(z_n) \rightarrow \partial^k f(z_0)$
negative_passages.docid: 30484
negative_passages.text: Radius of convergence and uniformly convergence
negative_passages.docid: 100580
negative_passages.text: Proof that a sequence converges.
negative_passages.docid: 144957
negative_passages.text: Uniform convergence of a function
negative_passages.docid: 110415
negative_passages.text: Proving a sequence of step functions converges pointwise to a function $f$.