query: Closed form expression for for $\sum\limits_{i=0}^{\infty} i^2\cdot x^i$
positive_passages.docid: 157972
positive_passages.text: Find a closed form expression for $\sum\limits_{i=0}^{\infty} i^2\cdot x^i$
negative_passages.docid: 141390
negative_passages.text: Closed form for $\sum_{n=-\infty}^\infty \frac{1}{(z+n)^2+a^2}$
negative_passages.docid: 153465
negative_passages.text: Is there a closed form expression for $1 + x + x^{4} + x^{9}+x^{16}+x^{25} +..+x^{k^2}$?
negative_passages.docid: 69439
negative_passages.text: Infinite Sum of algebraic expression
negative_passages.docid: 6416
negative_passages.text: How can I evaluate $\sum_{n=0}^\infty(n+1)x^n$?
negative_passages.docid: 27901
negative_passages.text: Proving $\sum\limits_{i=1}^k | \langle x,v_i \rangle \langle y,v_i\rangle| \leq \|x\|\cdot \|y\|$
negative_passages.docid: 7063
negative_passages.text: How to compute the  formula $\sum  \limits_{r=1}^d r \cdot 2^r$?
negative_passages.docid: 135218
negative_passages.text: Closed Form for Factorial Sum
negative_passages.docid: 110262
negative_passages.text: Finding a closed formula for $1\cdot2\cdot3\cdots k +\dots + n(n+1)(n+2)\cdots(k+n-1)$
negative_passages.docid: 65653
negative_passages.text: Find a closed form of the series $\sum_{n=0}^{\infty} n^2x^n$
negative_passages.docid: 145798
negative_passages.text: Generalizing $\sum \limits_{n=1}^{\infty }n^{2}/x^{n}$ to $\sum \limits_{n=1}^{\infty }n^{p}/x^{n}$
negative_passages.docid: 119606
negative_passages.text: Closed form of summation
negative_passages.docid: 69045
negative_passages.text: Solving this summation: $\sum_{i=1}^k i\cdot2^i$
negative_passages.docid: 99314
negative_passages.text: Closed form of infinite product $ \prod\limits_{k=0}^\infty \left(1+\frac{1}{2^{2^k}}\right)$
negative_passages.docid: 23726
negative_passages.text: A closed form for $1^{2}-2^{2}+3^{2}-4^{2}+ \cdots + (-1)^{n-1}n^{2}$
negative_passages.docid: 109059
negative_passages.text: Evaluate $\lim\limits_{n\to \infty}\frac{1}{n+1}+\frac{1}{n+2}+\cdots+\frac{1}{6n}$
negative_passages.docid: 69084
negative_passages.text: What is the closed form for $\sum_{n=1}^\infty \frac1n - \frac1{n+1/p}$?