query: Can $s_n=1+x+x^2+x^4+x^8+\ldots+x^{2^n}$ be simplified?
positive_passages.docid: 149352
positive_passages.text: What is the Riemann surface of $y=\sqrt{z+z^2+z^4+\cdots +z^{2^n}+\cdots}$?
negative_passages.docid: 105395
negative_passages.text: Minimal polynomial of $1 + 2^{1/3} + 4^{1/3}$
negative_passages.docid: 51518
negative_passages.text: Is $\sqrt[3]{p+q\sqrt{3}}+\sqrt[3]{p-q\sqrt{3}}=n$, $(p,q,n)\in\mathbb{N} ^3$ solvable?
negative_passages.docid: 137010
negative_passages.text: What are integers $x$ and $n$ such as $ x^4+x^3+x^2+x+1 = n^2$?
negative_passages.docid: 39909
negative_passages.text: Getting a closed form from $\sum_{i=1}^{n-1} \sum_{j=i+1}^{n} \sum_{k=1}^{j} 1$
negative_passages.docid: 158004
negative_passages.text: A formula for $1^4+2^4+...+n^4$
negative_passages.docid: 34059
negative_passages.text: $(a^{2^n}+1,a^{2^m}+1)=1 or 2$
negative_passages.docid: 5043
negative_passages.text: Show that $2^n>1+n\sqrt{2^{n-1}}$
negative_passages.docid: 116722
negative_passages.text: Simplifying $\big(\sum_{i=0}^n\binom{k}{i}\binom{M-k}{n-i}\frac{k-i}{M-n}\big)/{\binom{M}{n}}$
negative_passages.docid: 146753
negative_passages.text: Find $x$ such that $(x^2 + 4x + 3)^x + (2x + 4)^x = (x^2 + 4x + 5)^x$
negative_passages.docid: 89705
negative_passages.text: How to solve $a_n = 2a_{n-1} + 1, a_0 = 0, a_1 = 1$?
negative_passages.docid: 111805
negative_passages.text: If $a_{1}=1$ and $a_{n+1}=1+\frac{n}{a_{n}}$, then $a_{n}=\sqrt{n}+\frac{1}{2}-\frac{1}{8\sqrt{n}}+o\left(\frac{1}{\sqrt{n}}\right)$
negative_passages.docid: 135747
negative_passages.text: Prove $x^{rs}-1=(x^s-1)(x^{s(r-1)}+...+x^s+1)$
negative_passages.docid: 99843
negative_passages.text: How to simplify $ \sum_{k=0}^{\infty} \binom{k + r - 1}{k} x^k$
negative_passages.docid: 157552
negative_passages.text: Find the coefficient of $x^n$ simply by using binomial theorem
negative_passages.docid: 100159
negative_passages.text: How to simplify $\frac{1+\frac{1}{2^p} + \frac{1}{3^p} + \frac{1}{4^p} + \cdots}{1 - \frac{1}{2^p} + \frac{1}{3^p} - \frac{1}{4^p} + \cdots}$
negative_passages.docid: 54355
negative_passages.text: $1+x+\ldots+x^n$ perfect square