query: Calculate $\sum_{i=1}^n\sin(\frac{\pi\ i}{2n})$ and $\sum_{i=1}^n\sin(\frac{\pi\ i-\pi}{2n})$
positive_passages.docid: 5080
positive_passages.text: How can we sum up $\sin$ and $\cos$ series when the angles are in arithmetic progression?
negative_passages.docid: 121554
negative_passages.text: Finding $\sum\frac{1}{2^n(n+1)}$
negative_passages.docid: 17168
negative_passages.text: Find the value of $\sin\frac{2\pi}{7}+\sin\frac{4\pi}{7}+\sin\frac{8\pi}{7}$
negative_passages.docid: 30518
negative_passages.text: Formula for $\sum_{k=1}^n \frac{1}{k(k+1)(k+2)}$?
negative_passages.docid: 118456
negative_passages.text: Find $\sum_{n=1}^{\infty}\tan^{-1}\frac{2}{n^2}$
negative_passages.docid: 29170
negative_passages.text: Find the sum of the series $\sum \frac{1}{n(n+1)(n+2)}$
negative_passages.docid: 55128
negative_passages.text: Evaluation of $\sin \frac{\pi}{7}\cdot \sin \frac{2\pi}{7}\cdot \sin \frac{3\pi}{7}$
negative_passages.docid: 66568
negative_passages.text: Number Theory : Show that $\sum_{i=0}^\infty$ $ [\frac{n}{2^i}+\frac{1}{2}]$ $=$ $2n$
negative_passages.docid: 133955
negative_passages.text: Compute: $\sum_{k=1}^{\infty}\sum_{n=1}^{\infty} \frac{1}{k^2n+2nk+n^2k}$
negative_passages.docid: 47572
negative_passages.text: Evaluate $ \sum_{n=1}^{\infty} \frac{\sin \ n}{ n } $ using the fourier series
negative_passages.docid: 136444
negative_passages.text: Evaluating $\sum_{n=0}^\infty\frac{(-1)^n}{3n+1}$
negative_passages.docid: 34637
negative_passages.text: Evaluating $\sum\frac{\sin(n)}{n^a}$
negative_passages.docid: 26446
negative_passages.text: Find the sum : $\displaystyle\sum_{i=0}^n \frac{2^i}{1+x^{2^{i}}}$
negative_passages.docid: 49028
negative_passages.text: Find the sum : $\frac{1}{\cos0^\circ\cos1^\circ}+\frac{1}{\cos1^\circ \cos2^\circ} +\frac{1}{\cos2^\circ \cos3^\circ}+......+$
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: 112036
negative_passages.text: sum of series $\frac{n}{1\cdot 2 \cdot 3}+\frac{n-1}{2\cdot 3\cdot 4}+\frac{n-2}{3\cdot 4 \cdot 5}+\cdots \cdots n$ terms
negative_passages.docid: 153989
negative_passages.text: How to evaluate the sum $\frac{1}{\sqrt{n}}+\frac{1}{\sqrt{2n}}+\cdots+\frac{1}{\sqrt{n^2}}$ when $n$ grows?