query: Calculate the series $\sum_{n=1}^{\infty} \frac{x^n}{(3n)!}$
positive_passages.docid: 17172
positive_passages.text: Series $\frac{x^{3n}}{(3n)!} $ find sum using differentiation
negative_passages.docid: 93690
negative_passages.text: How to obtain the sum of the following series? $\sum_{n=1}^\infty{\frac{n^2}{2^n}}$
negative_passages.docid: 67731
negative_passages.text: Calculate the sum of infinite series with general term $\frac{n^2}{2^n}$.
negative_passages.docid: 17686
negative_passages.text: Evaluate the infinite series $\sum_{r=1}^{\infty} \frac{2^{-r}}{r^{2}}$
negative_passages.docid: 8905
negative_passages.text: Sum the series $\frac{3}{1⋅2⋅4}+\frac{4}{2⋅3⋅5}+ \frac{5}{3⋅4⋅6}+...\text{(upto n terms)}$
negative_passages.docid: 53658
negative_passages.text: Find the sum series $\sum_{n=1}^{+\infty} \frac{(-1)^{n-1}(2n-1)}{2^{n-1}}$
negative_passages.docid: 158737
negative_passages.text: What is the value of the series $\sum\limits_{n=1}^\infty \frac{(-1)^n}{n^2}$?
negative_passages.docid: 61850
negative_passages.text: Compute $\sum_{k=0}^{\infty}\frac{1}{2^{k!}}$
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: 92754
negative_passages.text: Closed form for the series: $\sum_{n=1}^{\infty}x^{n^2}$
negative_passages.docid: 135927
negative_passages.text: Calculating $\sum_{n=1}^\infty\frac{1}{(n-1)!(n+1)}$
negative_passages.docid: 28378
negative_passages.text: Find the infinite sum of the series $\sum_{n=1}^\infty \frac{1}{n^2 +1}$
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: 7177
negative_passages.text: Find sum of series $ \sum_{n=1}^{\infty} (n\cdot \ln \frac{2n+1}{2n-1} - 1) $
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: 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: 135032
negative_passages.text: Nature of the series $\sum\limits_{n=3}^{\infty} \frac{1}{(\log\log n)^{\log n}}$