query: $\sum_{n=1}^{\infty}\frac{\sin nx}{n}$
positive_passages.docid: 26541
positive_passages.text: Is $\sum_{n=1}^{\infty}{\frac{\sin(nx)}n}$ continuous?
negative_passages.docid: 72502
negative_passages.text: Evaluate $\sum_{n=1}^\infty nx^{n-1}$
negative_passages.docid: 74120
negative_passages.text: Find the value of $\sum_{n=1}^{\infty} \frac{2}{n}-\frac{4}{2n+1}$
negative_passages.docid: 78712
negative_passages.text: Prove that $\frac{1}{\sin^2 z } = \sum\limits_{n= -\infty} ^ {+\infty} \frac{1}{(z-\pi n)^2} $
negative_passages.docid: 32823
negative_passages.text: Prove $\forall n \in \mathbb{N}: \int_{0}^{\frac{\pi}{2}} |\frac{\sin(nx)}{x}|dx \geq \frac{2}{\pi}\sum_{k=1}^{n}\frac{1}{k}$
negative_passages.docid: 55339
negative_passages.text: Find the sum $\sum_{n=1}^{\infty}\frac{ 1}{n^{2}(2n-1)}$
negative_passages.docid: 59485
negative_passages.text: Infinite Series: $\sum_{n=1}^\infty \frac{1}{2^nn}$
negative_passages.docid: 95353
negative_passages.text: Does $\sum_{n=1}^\infty \frac{\cos{(\sqrt{n})}}{n}$ converge?
negative_passages.docid: 49262
negative_passages.text: Evaluation of Sum of $ \sum_{n=1}^{\infty}\frac{\sin (n)}{n}$.
negative_passages.docid: 137249
negative_passages.text: find $\sum_{k=2}^{\infty}\frac{1}{k^2-1}$
negative_passages.docid: 53658
negative_passages.text: Find the sum series $\sum_{n=1}^{+\infty} \frac{(-1)^{n-1}(2n-1)}{2^{n-1}}$
negative_passages.docid: 78542
negative_passages.text: What is $\sum_{n=1}^{\infty} \frac{n}{2^{\sqrt{n}}}$?
negative_passages.docid: 78473
negative_passages.text: Showing $ \sum_{n=0}^{\infty} \frac{1}{(3n+1)(3n+2)}=\frac{\pi}{3\sqrt{3}}$
negative_passages.docid: 47706
negative_passages.text: Find the value of $ \sum_{n=1}^{\infty} \frac{n^3}{3^n} $
negative_passages.docid: 149360
negative_passages.text: convergence of $ \sum_{k=1}^\infty \sin^2(\frac 1 k)$
negative_passages.docid: 93690
negative_passages.text: How to obtain the sum of the following series? $\sum_{n=1}^\infty{\frac{n^2}{2^n}}$
negative_passages.docid: 110055
negative_passages.text: Convergence of the series $\sum_{n=1}^{\infty}((1/n)-\sin(1/n))$..?