query: Ramanujan summation Series
positive_passages.docid: 4340
positive_passages.text: Why does $1+2+3+\cdots = -\frac{1}{12}$?
negative_passages.docid: 74117
negative_passages.text: Find the sum of series $\sum_{n=0}^{\infty}\frac{z^{kn}}{(kn)!}$
negative_passages.docid: 154183
negative_passages.text: Proof of a Ramanujan Integral
negative_passages.docid: 130945
negative_passages.text: Summation using residues
negative_passages.docid: 120988
negative_passages.text: Infinite Series $\sum 1/(n(n+1))$
negative_passages.docid: 149409
negative_passages.text: Is the series $\sum_{1}^{\infty}\frac{1}{p_{j}}$ where $p_{j}$ is the $j$th prime convergent?
negative_passages.docid: 71824
negative_passages.text: Finding the sum of the series $\frac{1}{1!}+\frac{1+2}{2!}+\frac{1+2+3}{3!}+ \ldots$
negative_passages.docid: 107433
negative_passages.text: Prove the sum to n terms of the series
negative_passages.docid: 93837
negative_passages.text: How to compute infinite series $\sum_{n=0}^{\infty} ne^{-n}$
negative_passages.docid: 49936
negative_passages.text: Various evaluations of the series $\sum_{n=0}^{\infty} \frac{(-1)^n}{(2n+1)^3}$
negative_passages.docid: 134610
negative_passages.text: Find the sum of finite series $S=\sum_{k=1}^{2015}{(-1)^{\frac{k(k+1)}{2}}}k$
negative_passages.docid: 139221
negative_passages.text: Compute the series $\sum_{n=1}^{+\infty} \frac{1}{n^3\sin(n\pi\sqrt{2})}.$
negative_passages.docid: 150928
negative_passages.text: Summation of a trigonometric series - $\frac{\sin n}{n}$
negative_passages.docid: 83641
negative_passages.text: The sum of the series $\frac{15}{16}+\frac{15}{16} \times \frac{21}{24}+\frac{15}{16} \times \frac{21}{24} \times \frac{27}{32}+\dots$
negative_passages.docid: 48446
negative_passages.text: Summation involving a factorial: $1 + \sum_{j=1}^{n} j!j$
negative_passages.docid: 148883
negative_passages.text: Sum of the series $\frac{1}{2\cdot 4}+\frac{1\cdot3}{2\cdot4\cdot6}+\dots$
negative_passages.docid: 119987
negative_passages.text: Show the series $ \sum_{j=1}^{\infty} \frac{(2^j)+ j}{(3^j) - j} $ converges