query: Closed-form term for $\sum_{i=1}^{\infty} i q^i$
positive_passages.docid: 6416
positive_passages.text: How can I evaluate $\sum_{n=0}^\infty(n+1)x^n$?
negative_passages.docid: 47753
negative_passages.text: Closed form of series with factorial-squared denominator?
negative_passages.docid: 84147
negative_passages.text: Evaluating $\sum_{n=1}^\infty \frac{2^{2n-1}}{5^{n+1}}$
negative_passages.docid: 326
negative_passages.text: Find $\sum_{k=1}^{\infty}\frac{1}{2^{k+1}-1}$
negative_passages.docid: 81589
negative_passages.text: Find the sum of $\sum_{k=0}^{\infty} 1/[(r+2k+2)(s+2k+2)]$
negative_passages.docid: 70390
negative_passages.text: is there a closed form expression for the following matrix infinite series
negative_passages.docid: 127267
negative_passages.text: Evaluation of $\sum_{n=1}^{\infty}\frac{1}{n(2n+1)}=2-2\ln(2)$
negative_passages.docid: 70248
negative_passages.text: Closed-form expression for $\sum_{k=0}^n\binom{n}kk^p$ for integers $n,\,p$
negative_passages.docid: 19914
negative_passages.text: Closed form for $\sum_{n=0}^{\infty} \binom{n+k}{k} x^n$ (Negative Binomial Theorem)
negative_passages.docid: 57759
negative_passages.text: Determining the infinite sum $\sum\limits_{n=0}^{\infty}\frac{(-1)^n}{2n+1}$
negative_passages.docid: 119606
negative_passages.text: Closed form of summation
negative_passages.docid: 43903
negative_passages.text: Find the sum for $\sum_{n=1}^{\infty}(-1)^{(n+1)}\frac{2n+1}{3^n} $
negative_passages.docid: 72502
negative_passages.text: Evaluate $\sum_{n=1}^\infty nx^{n-1}$
negative_passages.docid: 42736
negative_passages.text: Is there a closed form for $\sum_{k=0}^n \frac{x^k}{k!}$?
negative_passages.docid: 138313
negative_passages.text: How to sum $\sum_{n=1}^{\infty} \frac{1}{n^2 + a^2}$?
negative_passages.docid: 97266
negative_passages.text: Summation by parts (finite calculus) of $\sum\limits_{i=0}^{n}i\cdot a^i$
negative_passages.docid: 67271
negative_passages.text: $\sum_{n=-\infty}^{\infty}\frac{1}{(u +n)^2}=\frac{\pi^2}{(\sin \pi u)^2}$