query: Finding a closed form for $\cos{x}+\cos{3x}+\cos{5x}+\cdots+\cos{(2n-1)x}$
positive_passages.docid: 9479
positive_passages.text: $\sum \cos$ when angles are in arithmetic progression
negative_passages.docid: 46665
negative_passages.text: Solving $\cos x+\sin x-1=0$
negative_passages.docid: 123507
negative_passages.text: How to find the closed form of multiplications of exponentials?
negative_passages.docid: 86454
negative_passages.text: How to prove $\cos\left(\pi\over7\right)-\cos\left({2\pi}\over7\right)+\cos\left({3\pi}\over7\right)=\cos\left({\pi}\over3 \right)$
negative_passages.docid: 128608
negative_passages.text: Closed form for the series $a+a^p+(a^p)^p+\dots$
negative_passages.docid: 65698
negative_passages.text: Proving $\sum\limits_{k=0}^{n}\cos(kx)=\frac{1}{2}+\frac{\sin(\frac{2n+1}{2}x)}{2\sin(x/2)}$
negative_passages.docid: 10141
negative_passages.text: Find closed form expression for series expansion coefficients
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: 105238
negative_passages.text: Proving $\tan(\theta_1+\theta_2+\cdots+\theta_n)$ has the form $\frac{S_1-S_3+S_5+\cdots}{1-S_2+S_4+\cdots}$
negative_passages.docid: 65648
negative_passages.text: Different ways to come up with $1+2+3+\cdots +n=\frac{n(n+1)}{2}$
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: 60902
negative_passages.text: Find general solution for the equation $1 + 2 + \cdots + (n − 1) = (n + 1) + (n + 2) + \cdots + (n + r) $
negative_passages.docid: 74143
negative_passages.text: Simplifying and evaluating $\cot 70^\circ+4\cos 70^\circ$
negative_passages.docid: 83346
negative_passages.text: Finding a closed form $x_n$ for the recurrence relation $x_{n+2} = px_{n+1} + qx_n + r$
negative_passages.docid: 42736
negative_passages.text: Is there a closed form for $\sum_{k=0}^n \frac{x^k}{k!}$?
negative_passages.docid: 63155
negative_passages.text: Express $1+2\cos a$ as a product
negative_passages.docid: 12423
negative_passages.text: "Closed" form for $\sum \frac{1}{n^n}$