query: Find sum of series $\frac{1}{6} + \frac{5}{6 \cdot 12} + \frac{5\cdot 8}{6 \cdot 12 \cdot 18} + \dotsb$
positive_passages.docid: 95786
positive_passages.text: Sum $\frac{1}{6} + \frac{5}{6\cdot 12} + \frac{5\cdot 8}{6\cdot 12\cdot 18} + \frac{5\cdot 8\cdot 11}{6\cdot 12\cdot 18\cdot 24}+\ldots$
negative_passages.docid: 142985
negative_passages.text: Finding sum of series $\sum^{\infty}_{k=0}\frac{(k+1)(k+2)}{2^k}$
negative_passages.docid: 42271
negative_passages.text: Infinite Series $1+\frac12-\frac23+\frac14+\frac15-\frac26+\cdots$
negative_passages.docid: 148883
negative_passages.text: Sum of the series $\frac{1}{2\cdot 4}+\frac{1\cdot3}{2\cdot4\cdot6}+\dots$
negative_passages.docid: 115162
negative_passages.text: Establish convergence of the series: $1-\frac{1}{2}-\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}-...$
negative_passages.docid: 67434
negative_passages.text: Finding the infinite series: $3 \cdot \frac{9}{11} + 4 \cdot \left(\frac{9}{11}\right)^2 + 5 \cdot \left(\frac{9}{11}\right)^3 + \cdots$?
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: 100936
negative_passages.text: What is the sum of this series: $\frac{2}{\pi}\sum_{k=1}^{\infty}\frac{(-1)^{k-1}}{2k-1}$
negative_passages.docid: 25426
negative_passages.text: A sum of series problem: $\frac{3}{1!+2!+3!} + \frac{4}{2!+3!+4!} + \cdots + \frac{2008}{2006!+2007!+2008!}$
negative_passages.docid: 141357
negative_passages.text: Is $1+2+3+4+\cdots=-\frac{1}{12}$ the unique ''value'' of this series?
negative_passages.docid: 7177
negative_passages.text: Find sum of series $ \sum_{n=1}^{\infty} (n\cdot \ln \frac{2n+1}{2n-1} - 1) $
negative_passages.docid: 102339
negative_passages.text: How to compute the sum of a series
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: 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: 133420
negative_passages.text: Computing the binomial series: $\binom{n}{2}\cdot2^2+\binom{n}{4}\cdot2^4+\binom{n}{6}\cdot2^6+\cdots+ \binom{n}{n}\cdot2^n$
negative_passages.docid: 58262
negative_passages.text: Find the sum of the series $1+\frac{1}{3}\cdot\frac{1}{4}+\frac{1}{5}\cdot\frac{1}{4^2}+\frac{1}{7}\cdot\frac{1}{4^3}+\cdots$
negative_passages.docid: 127189
negative_passages.text: sum of this series: $\sum_{n=1}^{\infty}\frac{1}{4n^2-1}$