query: Infinite sums of reciprocal power: $\sum\frac1{n^{2}}$ over odd integers
positive_passages.docid: 26474
positive_passages.text: how can we show $\frac{\pi^2}{8} = 1 + \frac1{3^2} +\frac1{5^2} + \frac1{7^2} + …$?
negative_passages.docid: 126304
negative_passages.text: Determining bounds for the sum $\sum\limits_{n=1}^\infty \frac{1}{2^n - 3^n }$
negative_passages.docid: 140614
negative_passages.text: Show that $\sum^\infty_{n=m}\frac{1}{n^2} = O(\frac{1}{m})$
negative_passages.docid: 18064
negative_passages.text: Sum of reciprocals of numbers with certain terms omitted
negative_passages.docid: 110975
negative_passages.text: Summation of reciprocals
negative_passages.docid: 125933
negative_passages.text: On the series $\sum \limits_{n=2}^{\infty} \frac{(-1)^n}{n \log n}$
negative_passages.docid: 140458
negative_passages.text: Infinite summation involving exponents
negative_passages.docid: 70677
negative_passages.text: Finite Sum of Power?
negative_passages.docid: 45672
negative_passages.text: Even/Odd Binomial Coefficients
negative_passages.docid: 13291
negative_passages.text: Proving $\sum_{k=1}^n\frac1{\sqrt k}<2\sqrt n$ by induction
negative_passages.docid: 117056
negative_passages.text: How to show $\sum_{n=1}^{\infty}\frac{H_{n+1}}{n(n+1)}=2$?
negative_passages.docid: 153226
negative_passages.text: Proof of $\sum_{k = 1}^{n} \frac{1}{k^{2}} < 2 - \frac{1}{n}$
negative_passages.docid: 42216
negative_passages.text: Sum of infinite series $\sum_{i=1}^{\infty} \frac 1 {i(i+1)(i+2)...(i+n)}$
negative_passages.docid: 78473
negative_passages.text: Showing $ \sum_{n=0}^{\infty} \frac{1}{(3n+1)(3n+2)}=\frac{\pi}{3\sqrt{3}}$
negative_passages.docid: 143343
negative_passages.text: The series of reciprocals of the integers that do not contain 9 in their decimal representation
negative_passages.docid: 6436
negative_passages.text: Proving an alternating Euler sum: $\sum_{k=1}^{\infty} \frac{(-1)^{k+1} H_k}{k} = \frac{1}{2} \zeta(2) - \frac{1}{2} \log^2 2$
negative_passages.docid: 155005
negative_passages.text: How to show $\sum_{k=n}^\infty{\frac{1}{k!}} \leq \frac{2}{n!}$