query: Find the sun of ${x\over(x+1)}+{x^2\over(x+1)(x^2+1)}+{x^4\over(x+1)(x^2+1)(x^4+1)}+...$
positive_passages.docid: 143236
positive_passages.text: $ S_{n}=\frac{x}{x+1}+\frac{x^2}{(x+1)(x^2+1)}+...........+\frac{x^{2^{n}}}{(x+1)(x^2+1)...(x^{2^{n}}+1)}$
negative_passages.docid: 109102
negative_passages.text: Determine all real polynomials with $P(0)=0$ and $P(x^2+1)=(P(x))^2+1$
negative_passages.docid: 96036
negative_passages.text: If $X$ takes on a Gamma Distribution, how can I find $X^2$, $X^3$, etc?
negative_passages.docid: 49744
negative_passages.text: Find remainder of division of $x^3$ by $x^2-x+1$
negative_passages.docid: 7201
negative_passages.text: Prove that $x_1^2+x_2^2+x_3^2=1$ yields $ \sum_{i=1}^{3}\frac{x_i}{1+x_i^2} \le \frac{3\sqrt{3}}{4} $
negative_passages.docid: 2205
negative_passages.text: Solving $x^{x^x}=c$ with Lambert's W function
negative_passages.docid: 113250
negative_passages.text: If $x+{1\over x} = r $ then what is $x^3+{1\over x^3}$?
negative_passages.docid: 77864
negative_passages.text: Find $P(12)$ when $P(x)={1\over(x+1)}$, for $x=0,1,2,......11$
negative_passages.docid: 33184
negative_passages.text: Something strange about $\sqrt{ 4+ \sqrt{ 4 + \sqrt{ 4-x}}}=x$ and its friends
negative_passages.docid: 42391
negative_passages.text: Calculate $\tan9^{\circ}-\tan27^{\circ}-\tan63^{\circ}+\tan81^{\circ}$
negative_passages.docid: 53725
negative_passages.text: Factor $(x+y)^4+x^4+y^4$
negative_passages.docid: 76685
negative_passages.text: Determine $\text{Aut}(S)$ where $S = \mathbb{Q}[x]/(x^2)$
negative_passages.docid: 43320
negative_passages.text: Find the sum of the power series $\sum_{n=1}^\infty n*(n+1)*x^n$
negative_passages.docid: 31317
negative_passages.text: If we know $x+y+z=1$, $x^2+y^2+z^2=2$, and $x^3+y^3+z^3=3$, how to find $x^4+y^4+z^4$?
negative_passages.docid: 2300
negative_passages.text: Determine the remainder when $f(x) = 3x^5 - 5x^2 + 4x + 1$ is divided by $(x-1)(x+2)$
negative_passages.docid: 64448
negative_passages.text: Find a quadratic equation with root $x_1^2$ and $x_2^2$
negative_passages.docid: 115513
negative_passages.text: Find the minimum of $\sqrt{(x+1)^2+(y-1)^2}+\sqrt{(x+2)^2+(y+2)^2}+\sqrt{(x-1)^2+(y+1)^2}$ For real $x,y$