query: Sum of $50$ terms of $\cot^{-1}3+\cot^{-1}7+\cot^{-1}13+\cot^{-1}21+.....$
positive_passages.docid: 4573
positive_passages.text: Explicitly finding the sum of $\arctan(1/(n^2+n+1))$
negative_passages.docid: 62271
negative_passages.text: Find the sum of the series: $\cos^3 \alpha +\cos^3 {3\alpha} + \cos^3 {5\alpha}+....+\cos^3 {(2n-1)\alpha}$.
negative_passages.docid: 89758
negative_passages.text: Is there a formula for $(1+i)^n+(1-i)^n$?
negative_passages.docid: 69439
negative_passages.text: Infinite Sum of algebraic expression
negative_passages.docid: 74143
negative_passages.text: Simplifying and evaluating $\cot 70^\circ+4\cos 70^\circ$
negative_passages.docid: 14399
negative_passages.text: Calculate $\sum_{k=1}^n (-1)^{k+1} \binom{n}{k}\frac{1}{k}$
negative_passages.docid: 83641
negative_passages.text: The sum of the series $\frac{15}{16}+\frac{15}{16} \times \frac{21}{24}+\frac{15}{16} \times \frac{21}{24} \times \frac{27}{32}+\dots$
negative_passages.docid: 43903
negative_passages.text: Find the sum for $\sum_{n=1}^{\infty}(-1)^{(n+1)}\frac{2n+1}{3^n} $
negative_passages.docid: 18064
negative_passages.text: Sum of reciprocals of numbers with certain terms omitted
negative_passages.docid: 114414
negative_passages.text: Sum of $\sum_{k=1}^n\sin{k\theta}$
negative_passages.docid: 38541
negative_passages.text: How many solutions are there to $x_1 + x_2 + ... + x_5 = 21$?
negative_passages.docid: 138172
negative_passages.text: Find the sum to n terms of the series $\frac{1}{1.2.3}+\frac{3}{2.3.4}+\frac{5}{3.4.5}+\frac{7}{4.5.6}+\cdots$..
negative_passages.docid: 30724
negative_passages.text: Summation splitting: $\sum_{n=1}^{\infty} \frac{n}{3\cdot 5\cdot 7 \dots (2n+1)}$
negative_passages.docid: 105117
negative_passages.text: $1 + \frac{1}{3}\frac{1}{4} + \frac{1}{5}\frac{1}{4^2} + \frac{1}{7}\frac{1}{4^3} + ..........$
negative_passages.docid: 124135
negative_passages.text: A general formula for $\sum (k-1)(k-2)(k-3)$?
negative_passages.docid: 125876
negative_passages.text: Sum and Product of Infinite Radicals
negative_passages.docid: 85571
negative_passages.text: How do I simplify $\sqrt{3}(\cot 70^\circ + 4 \cos 70^\circ )$?