query: How can I prove that the following series does not converge uniformly.
positive_passages.docid: 17048
positive_passages.text: $\sum_{n=1}^\infty\frac{z^n}{n}$ does not converge uniformly on $\mathbb{D}$.
negative_passages.docid: 63380
negative_passages.text: Show that the series $\sum_{n=2}^{\infty} \frac{1}{n\, (\log n)^s}$ converges for $s >1$ and diverges for $s=1$
negative_passages.docid: 61598
negative_passages.text: Convergence of semi-telescopic series $\sum\limits_{k=1}^\infty\frac{1}{k(k+1)(k+2)}$
negative_passages.docid: 129078
negative_passages.text: Proving the series $\sum_{n=0}^{\infty}\sin(e\pi n!)$ converges
negative_passages.docid: 40079
negative_passages.text: Convergence of the series $\sum_n \frac{n^{\log(n)}}{\log(n)^n}$
negative_passages.docid: 132018
negative_passages.text: problem involving series that converges depending on another series converging
negative_passages.docid: 72900
negative_passages.text: What is the best way to show that the exponential sequence doesn't uniformally converge on an unbounded interval
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: 60217
negative_passages.text: Proof: Series converges $\implies $ the limit of the sequence is zero
negative_passages.docid: 15031
negative_passages.text: Convergence test of the series $\sum\sin100n$
negative_passages.docid: 64076
negative_passages.text: how to show that this complex series converge?
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: 7078
negative_passages.text: If $\sum_n \sqrt{a_n a_{n+1}}$ converges, then $\sum_n a_n$ might not converge.
negative_passages.docid: 15803
negative_passages.text: Does the series $\sum n!/n^n$ converge or diverge?
negative_passages.docid: 54376
negative_passages.text: Convergence of the series $\sqrt[n]n-1$
negative_passages.docid: 84181
negative_passages.text: Is there a cleaner proof of convergence for this almost-telescoping series
negative_passages.docid: 69989
negative_passages.text: Do the following series converge if $a_n>0$ and $ \sum_{n=1}^{\infty}a_n$ diverges?