query: $\zeta(4)=\sum_ {k=1}^{\infty}{\frac{1}{k^4}}$
positive_passages.docid: 15477
positive_passages.text: Nice proofs of $\zeta(4) = \frac{\pi^4}{90}$?
negative_passages.docid: 127189
negative_passages.text: sum of this series: $\sum_{n=1}^{\infty}\frac{1}{4n^2-1}$
negative_passages.docid: 152698
negative_passages.text: Evaluation of $\sum_{n=0}^{\infty}\frac{1}{(n^4+n^2+1)n!}$
negative_passages.docid: 17713
negative_passages.text: What's the value of $\sum\limits_{k=1}^{\infty}\frac{k^2}{k!}$?
negative_passages.docid: 104078
negative_passages.text: Calculate the sum of the infinite series $\sum_{n=0}^{\infty} \frac{n}{4^n}$
negative_passages.docid: 55061
negative_passages.text: Evaluating the sum after reordering an infinite series $1-\frac {1} {2}+\frac {1} {3}-\frac {1} {4}+\ldots $
negative_passages.docid: 60104
negative_passages.text: Evaluate $\sum_{k=1}^\infty\frac{x^k}{k(k+1)}$
negative_passages.docid: 100936
negative_passages.text: What is the sum of this series: $\frac{2}{\pi}\sum_{k=1}^{\infty}\frac{(-1)^{k-1}}{2k-1}$
negative_passages.docid: 26233
negative_passages.text: $[K(\zeta_n):K]=\phi(n)$?
negative_passages.docid: 79415
negative_passages.text: The series $\sum_{n=2}^{\infty }\frac{1}{\log (n!)}$
negative_passages.docid: 94943
negative_passages.text: Sum of series with addition: $\sum_{n=1}^\infty \frac{1}{n^2(n+1)}$
negative_passages.docid: 74120
negative_passages.text: Find the value of $\sum_{n=1}^{\infty} \frac{2}{n}-\frac{4}{2n+1}$
negative_passages.docid: 67271
negative_passages.text: $\sum_{n=-\infty}^{\infty}\frac{1}{(u +n)^2}=\frac{\pi^2}{(\sin \pi u)^2}$
negative_passages.docid: 16776
negative_passages.text: How to prove $\sum_{m=1}^\infty \sum_{n=1}^\infty \frac{1}{m^2+n^2}=+\infty$
negative_passages.docid: 119552
negative_passages.text: Summing Finitely Many Terms of Harmonic Series: $\sum_{k=a}^{b} \frac{1}{k}$
negative_passages.docid: 154544
negative_passages.text: Prove that $ \sum_{n=0}^\infty \frac{z^{2^n}}{1-z^{2^{n+1}}}=\frac{z}{1-z} $
negative_passages.docid: 52278
negative_passages.text: How to solve $\sum_{k=2}^\infty {\frac{1}{k^2-1}}$