query: The infinite series of $x^{n^2}$
positive_passages.docid: 47575
positive_passages.text: Compute the limit of $\sqrt{1-a}\sum\limits_{n=0}^{+\infty} a^{n^2}$ when $a\to1^-$
negative_passages.docid: 5650
negative_passages.text: Show $\ln2 = \sum_\limits{n=1}^\infty\frac1{n2^n}$
negative_passages.docid: 90696
negative_passages.text: Series in Real Analysis
negative_passages.docid: 56231
negative_passages.text: Infinite series for $e$...
negative_passages.docid: 17504
negative_passages.text: Divergent infinite series $n!e^n/n^n$ - simpler proof of divergence?
negative_passages.docid: 151477
negative_passages.text: computing the series $\sum_{n=1}^\infty \frac{1}{n^2 2^n}$
negative_passages.docid: 117863
negative_passages.text: Series $\sum_{n=1}^\infty \frac{n^n}{(n!)^2}$
negative_passages.docid: 158357
negative_passages.text: Infinite Product $\prod_{n=1}^\infty\left(1+\frac1{\pi^2n^2}\right)$
negative_passages.docid: 71240
negative_passages.text: The limit of a sum $\sum_{k=1}^n \frac{n}{n^2+k^2}$ as $n\rightarrow\infty$
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: 44706
negative_passages.text: Behavior of $\sum a_n x^n$ given $\sum |a_n - a_{n-1}| < \infty$
negative_passages.docid: 158756
negative_passages.text: Dividing an infinite power series by another infinite power series
negative_passages.docid: 6223
negative_passages.text: Problem regarding radius of convergence of $\sum n!x^{n^2}$.
negative_passages.docid: 23945
negative_passages.text: Infinite Series: Fibonacci/ $2^n$
negative_passages.docid: 64223
negative_passages.text: Infinite Series $\sum\limits_{n=1}^\infty\left(\frac{H_n}n\right)^2$
negative_passages.docid: 125876
negative_passages.text: Sum and Product of Infinite Radicals
negative_passages.docid: 28378
negative_passages.text: Find the infinite sum of the series $\sum_{n=1}^\infty \frac{1}{n^2 +1}$