query: What is the value of the following series
positive_passages.docid: 152557
positive_passages.text: Calculate $ \lim\limits_{n \to \infty} \sum\limits_{k=0}^n \frac{2^{k-1}}{a^{2k-1}+1} $
negative_passages.docid: 122236
negative_passages.text: How to compute the series: $\sum_{n=0}^{\infty} (-1)^{n-1}\binom{1/2}{n}$
negative_passages.docid: 69588
negative_passages.text: Convergence of a given series
negative_passages.docid: 113633
negative_passages.text: sum of series using mean value theorem
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: 45588
negative_passages.text: Summing a series with a changing power
negative_passages.docid: 90030
negative_passages.text: What would be the value of $\sum\limits_{n=0}^\infty \frac{1}{an^2+bn+c}$
negative_passages.docid: 17056
negative_passages.text: How to find answer to the sum of series $\sum_{n=1}^{\infty}\frac{n}{2^n} $
negative_passages.docid: 28378
negative_passages.text: Find the infinite sum of the series $\sum_{n=1}^\infty \frac{1}{n^2 +1}$
negative_passages.docid: 125148
negative_passages.text: Summation of series $\sum_{k=0}^\infty 2^k/\binom{2k+1}{k}$
negative_passages.docid: 3414
negative_passages.text: Value of Summation of $\log(n)$
negative_passages.docid: 25504
negative_passages.text: How to find sum of the infinite series $\sum_{n=1}^{\infty} \frac{1}{ n(2n+1)}$
negative_passages.docid: 30895
negative_passages.text: Compute the sum of the series $\sum_{n=1}^{\infty} \frac{1}{n \cdot 2^n}$
negative_passages.docid: 86353
negative_passages.text: when is this series convergent.
negative_passages.docid: 124440
negative_passages.text: Evaluate this power series
negative_passages.docid: 29170
negative_passages.text: Find the sum of the series $\sum \frac{1}{n(n+1)(n+2)}$
negative_passages.docid: 117843
negative_passages.text: Finding the sum of series $\sum_{n=0}^∞ \frac{2^n + 3^n}{6^n}$