query: Closed-form for $\sum_k r^{k^2}$?
positive_passages.docid: 153465
positive_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: 140462
negative_passages.text: Find a closed form for the power series $f_p(x)=\sum\limits_{n=0}^\infty\frac{n^p}{n!}x^n$
negative_passages.docid: 123955
negative_passages.text: How to compute $\sum\limits_{k=0}^n (-1)^k{2n-k\choose k}$?
negative_passages.docid: 110996
negative_passages.text: Sum of the form $r+r^2+r^4+\dots+r^{2^k} = \sum_{i=1}^k r^{2^i}$
negative_passages.docid: 114911
negative_passages.text: Evaluate $\sum_{k = 0}^{n} {n\choose k} k^m$
negative_passages.docid: 92754
negative_passages.text: Closed form for the series: $\sum_{n=1}^{\infty}x^{n^2}$
negative_passages.docid: 30518
negative_passages.text: Formula for $\sum_{k=1}^n \frac{1}{k(k+1)(k+2)}$?
negative_passages.docid: 125148
negative_passages.text: Summation of series $\sum_{k=0}^\infty 2^k/\binom{2k+1}{k}$
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: 147887
negative_passages.text: When do we have $ \lim_{n\to\infty}\sum_{k=1}^{n^2}\frac{n^{r-1}}{n^r+k^r}0$?
negative_passages.docid: 133160
negative_passages.text: Closed form for $\int_0^\infty\frac{1}{(1+x^2)^s}\,dx$ when $s\in (0.5,\infty)\setminus\mathbb{N}$
negative_passages.docid: 10222
negative_passages.text: Simplify $\sum (x_i- \mu)^2$
negative_passages.docid: 129801
negative_passages.text: Finding a closed form for $\sum^{n}_{k=1} \frac{k}{(k+1)!} $
negative_passages.docid: 56365
negative_passages.text: Evaluate $\sum\limits_{k=1}^{n} \frac{k}{2^k}$
negative_passages.docid: 119606
negative_passages.text: Closed form of summation
negative_passages.docid: 157972
negative_passages.text: Find a closed form expression for $\sum\limits_{i=0}^{\infty} i^2\cdot x^i$
negative_passages.docid: 119552
negative_passages.text: Summing Finitely Many Terms of Harmonic Series: $\sum_{k=a}^{b} \frac{1}{k}$