query: Show that $\sum_{n=1}^{\infty} \frac{1}{n^4} = \frac{\pi^4}{90}$
positive_passages.docid: 15477
positive_passages.text: Nice proofs of $\zeta(4) = \frac{\pi^4}{90}$?
negative_passages.docid: 80277
negative_passages.text: How to show that $\lim \frac{1}{n} \sum_{i=1}^n \frac{1}{i}=0 $?
negative_passages.docid: 33986
negative_passages.text: Calculate $\sum_{n=1}^{\infty}(\frac{1}{2n}-\frac{1}{n+1}+\frac{1}{2n+4})$
negative_passages.docid: 96961
negative_passages.text: A proof for the identity $\sum_{n=r}^{\infty} {n \choose r}^{-1} = \frac{r}{r-1}$
negative_passages.docid: 54661
negative_passages.text: How to find the sum $\sum\limits_{n=1}^{\infty}\frac{1}{n!(n^4+n^2+1)}$
negative_passages.docid: 41751
negative_passages.text: $\sum_{n=1}^\infty \frac{i^n}{n}$ converge?
negative_passages.docid: 52218
negative_passages.text: Show that $\sum_{n=1}^{\infty} \frac{(2n)!}{4^n(n!)^2}$ is divergent
negative_passages.docid: 55339
negative_passages.text: Find the sum $\sum_{n=1}^{\infty}\frac{ 1}{n^{2}(2n-1)}$
negative_passages.docid: 52987
negative_passages.text: $\sum_{n=-\infty}^{\infty}\frac{1}{(n+\alpha)^2}=\frac{\pi^2}{(\sin \pi \alpha)^2}$?
negative_passages.docid: 138313
negative_passages.text: How to sum $\sum_{n=1}^{\infty} \frac{1}{n^2 + a^2}$?
negative_passages.docid: 132126
negative_passages.text: Proving $\sum\limits_{n=1}^{\infty } \frac{\mu (n)}n=0$ where $\mu$ is the Möbius function
negative_passages.docid: 49052
negative_passages.text: Find $\sum_{n=1}^\infty \frac{n^3}{n!}$.
negative_passages.docid: 88292
negative_passages.text: Prove by induction that $\sum\limits_{i=1}^n \frac{1}{n+i} \leq \frac{3}{4}$
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: 24407
negative_passages.text: How to prove the Fibonacci sum $\sum \limits_{n=0}^{\infty}\frac{F_n}{p^n} = \frac{p}{p^2-p-1}$
negative_passages.docid: 145019
negative_passages.text: Prove that $\sum_{n=0}^\infty \frac{(-1)^n}{3n+1} = \frac{\pi}{3\sqrt{3}}+\frac{\log 2}{3}$
negative_passages.docid: 142218
negative_passages.text: $\sum_{n=1}^{\infty}\frac{1}{n^22^n}$ by integration or differentiation