query: Estimated value of $\sum \limits_{i=1}^{50} \frac{1}{2i-1}$?
positive_passages.docid: 143271
positive_passages.text: Finite sum of reciprocal odd integers
negative_passages.docid: 143368
negative_passages.text: Find the ratio of $\frac{\int_{0}^{1} \left(1-x^{50}\right)^{100} dx}{\int_{0}^{1} \left(1-x^{50}\right)^{101} dx}$
negative_passages.docid: 112950
negative_passages.text: Find the value of infinite series $\sum_{n=1}^{\infty} \tan^{-1}(2/n^2)$
negative_passages.docid: 130307
negative_passages.text: Limits under multiple \sum
negative_passages.docid: 28489
negative_passages.text: Estimating partial sums $\sum_{n = 1}^m \frac{1}{\sqrt{n}}$
negative_passages.docid: 6278
negative_passages.text: The value of $\sum_{1\leq l< m <n}^{} \frac{1}{5^l3^m2^n}$
negative_passages.docid: 76941
negative_passages.text: How do you find the value of $\sum_{r=0}^{44} \tan^2(2r+1)$?
negative_passages.docid: 54849
negative_passages.text: For what values of $\theta$ does $\sum_{1}^{\infty} \frac{e^{i n\theta}}{n}$ Converge?
negative_passages.docid: 123955
negative_passages.text: How to compute $\sum\limits_{k=0}^n (-1)^k{2n-k\choose k}$?
negative_passages.docid: 71240
negative_passages.text: The limit of a sum $\sum_{k=1}^n \frac{n}{n^2+k^2}$ as $n\rightarrow\infty$
negative_passages.docid: 42241
negative_passages.text: Evaluation of $\lim_{n\rightarrow \infty}\sum^{n}_{r=1}\frac{r}{n^2+n+r}$
negative_passages.docid: 57759
negative_passages.text: Determining the infinite sum $\sum\limits_{n=0}^{\infty}\frac{(-1)^n}{2n+1}$
negative_passages.docid: 62463
negative_passages.text: A pencil approach to find $\sum \limits_{i=1}^{69} \sqrt{\left( 1+\frac{1}{i^2}+\frac{1}{(i+1)^2}\right)}$
negative_passages.docid: 56265
negative_passages.text: limit $\lim\limits_{n\to\infty}\left(\sum\limits_{i=1}^{n}\frac{1}{\sqrt{i}} - 2\sqrt{n}\right)$
negative_passages.docid: 117383
negative_passages.text: What is the value of $\Gamma(\mathrm{i})$ ?
negative_passages.docid: 84147
negative_passages.text: Evaluating $\sum_{n=1}^\infty \frac{2^{2n-1}}{5^{n+1}}$
negative_passages.docid: 100936
negative_passages.text: What is the sum of this series: $\frac{2}{\pi}\sum_{k=1}^{\infty}\frac{(-1)^{k-1}}{2k-1}$