query: Where Is The Problem In Proving $1=2$ Through Continued Fractions
positive_passages.docid: 79274
positive_passages.text: $1=2$ | Continued fraction fallacy
negative_passages.docid: 136994
negative_passages.text: Proving :$\frac{1}{2ab^2+1}+\frac{1}{2bc^2+1}+\frac{1}{2ca^2+1}\ge1$
negative_passages.docid: 49851
negative_passages.text: when the sum of some fractions be $1$
negative_passages.docid: 44250
negative_passages.text: rational number solutions to $\frac{a}{a^2+1} + \frac{b}{b^2+1} = \frac{c}{c^2+1}$ with $abc\ne 0$
negative_passages.docid: 147528
negative_passages.text: Where's the error in this $2=1$ fake proof?
negative_passages.docid: 54059
negative_passages.text: Showing that $\frac{z^n}{1+z^{2n}}$ is real for $|z|=1$.
negative_passages.docid: 30478
negative_passages.text: How to prove that a number is irrational
negative_passages.docid: 74523
negative_passages.text: Proof by Cases involving divisibility
negative_passages.docid: 54296
negative_passages.text: How can I write Mathematica code for this continued fraction with alternating terms?
negative_passages.docid: 95057
negative_passages.text: Possible fake proof of $1= -1$
negative_passages.docid: 68771
negative_passages.text: Assume that $ 1a_1+2a_2+\cdots+na_n=1$, where the $a_j$ are real numbers.
negative_passages.docid: 39908
negative_passages.text: Finding the error in this proof that 1=2
negative_passages.docid: 36837
negative_passages.text: Prove $\frac{1+a^{2}}{1+b+c^{2}} +\frac{1+b^{2}}{1+c+a^{2}} +\frac{1+c^{2}}{1+a+b^{2}} \geq 2$
negative_passages.docid: 1002
negative_passages.text: Where is the flaw in this "proof" that 1=2? (Derivative of repeated addition)
negative_passages.docid: 105164
negative_passages.text: If $abc=1$, prove that $\frac{2}{(a+1)^2+b^2+1} + \frac{2}{(b+1)^2+c^2+1} + \frac{2}{(c+1)^2+a^2+1} \le 1$.
negative_passages.docid: 112512
negative_passages.text: How to prove that there are finitely many $n$ such that $f(1+1/n) = \frac{1}{n+1}$?
negative_passages.docid: 145152
negative_passages.text: How to prove that $\frac{x^2}{yz+2}+\frac{y^2}{zx+2}+\frac{z^2}{xy+2}\geq \frac{x+y+z}{3}$ holds for any $(x,y,z)\in[1,2]^3$