query: Let $A = \frac{1}{\frac{1}{2011}+\frac{1}{2012}+\frac{1}{2013}+\frac{1}{2014}+\frac{1}{2015}+\frac{1}{2016}}$.
positive_passages.docid: 150810
positive_passages.text: If $A=\frac{1}{\frac{1}{1980}+\frac{1}{1981}+\frac{1}{1982}+........+\frac{1}{2012}}\;,$ Then $\lfloor A \rfloor\;\;,$
negative_passages.docid: 154085
negative_passages.text: $\sum a_i \ln(b_i) \leq \sum a_i \ln(a_i)$ with $\sum a_i = \sum b_i = 1$
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: 37783
negative_passages.text: Proving that a set of 2016 natural numbers contain a non-empty set with a sum divisible by 2016
negative_passages.docid: 93756
negative_passages.text: $1+\frac{1}{2} +\frac{1}{3} +...+\frac{1}{p-1} =\frac{a}{b}$
negative_passages.docid: 140342
negative_passages.text: $\frac {1}{5}-\frac{1.4}{5.10}+\frac{1.4.7}{5.10.15}-\cdot\cdot\cdot\cdot\cdot\cdot\cdot$
negative_passages.docid: 95786
negative_passages.text: Sum $\frac{1}{6} + \frac{5}{6\cdot 12} + \frac{5\cdot 8}{6\cdot 12\cdot 18} + \frac{5\cdot 8\cdot 11}{6\cdot 12\cdot 18\cdot 24}+\ldots$
negative_passages.docid: 4547
negative_passages.text: How to solve $\frac{1}{1000.1998}+\frac{1}{1001.1997}+\cdots+\frac{1}{1998.1000}$
negative_passages.docid: 50972
negative_passages.text: Prove that $\sum_{x=1}^{n} \frac{1}{x (x+1)(x+2)} = \frac{1}{4} - \frac{1}{2 (n+1) (n+2)}$
negative_passages.docid: 42271
negative_passages.text: Infinite Series $1+\frac12-\frac23+\frac14+\frac15-\frac26+\cdots$
negative_passages.docid: 145882
negative_passages.text: How prove this $\frac{a}{(bc-a^2)^2}+\frac{b}{(ca-b^2)^2}+\frac{c}{(ab-c^2)^2}=0$
negative_passages.docid: 71299
negative_passages.text: Prove that $\frac{a}{b} < \frac{a+c}{b+d} <\frac{ c}{d}$
negative_passages.docid: 40524
negative_passages.text: Let $A \subseteq (0,\infty$) such that $\inf A>0$. Let $\frac{1}{A}=\{\frac{1}{a},a\in A\}$. Prove that $\sup \frac{1}{A}=\frac{1}{\inf A}$.
negative_passages.docid: 8666
negative_passages.text: Let us define a series $\{a(n)\}$ such that $a(n)= a(n-1) + \frac{1}{a(n-1)}$
negative_passages.docid: 105793
negative_passages.text: Solution of equation $\frac{x\cdot 2014^{\frac{1}{x}}+\frac{1}{x}\cdot 2014^x}{2} = 2014$
negative_passages.docid: 131847
negative_passages.text: $\frac{(x-1)(x+1)}{ (x+1)} \rightarrow (x-1)$ Domain Change
negative_passages.docid: 60309
negative_passages.text: Let X be a subset of {1,2,...,2014}...