query: Why is $\frac{n-1}{n}$ always in its simplest form?
positive_passages.docid: 151434
positive_passages.text: If integers $a$ and $b$ are not both zero, then $\gcd(a,b)=\gcd(a-b,b)$
negative_passages.docid: 153226
negative_passages.text: Proof of $\sum_{k = 1}^{n} \frac{1}{k^{2}} < 2 - \frac{1}{n}$
negative_passages.docid: 55994
negative_passages.text: Why do statisticians like "$n-1$" instead of "$n$"?
negative_passages.docid: 73102
negative_passages.text: Given the factors of $N$, is there a method for computing the factors of $N-1$ or $N+1$?
negative_passages.docid: 15164
negative_passages.text: Proof of $\sum^{2N}_{n=1} \frac{(-1)^{n-1}}{n} = \sum^{N}_{n=1} \frac{1}{N+n}$
negative_passages.docid: 482
negative_passages.text: Express $1 + \frac {1}{2} \binom{n}{1} + \frac {1}{3} \binom{n}{2} + \dotsb + \frac{1}{n + 1}\binom{n}{n}$ in a simplifed form
negative_passages.docid: 69498
negative_passages.text: What is $\sum_{r=0}^n \frac{(-1)^r}{\binom{n}{r}}$?
negative_passages.docid: 31907
negative_passages.text: Why does N[1.000 01, 10] return 1.00001, but N[1.000 001, 10] returns only 1.?
negative_passages.docid: 61670
negative_passages.text: Proving that $(b_n) \to b$ implies $\left(\frac{1}{b_n}\right) \to \frac{1}{b}$
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: 104646
negative_passages.text: Question on simplification of $\sum_{n=1}^{\infty}\frac{2}{(2n+1)(2n+3)}$?
negative_passages.docid: 109192
negative_passages.text: Intuitive reason why $ \frac1j > \int_{j}^{j+1} \frac1x dx $ for $j$ < $x$
negative_passages.docid: 146093
negative_passages.text: Why if $n \mid m$, then $(a^n-1) \mid (a^m-1)$?
negative_passages.docid: 63474
negative_passages.text: Showing $\sum_{i = 1}^n\frac1{i(i+1)} = 1-\frac1{n+1}$ without induction?
negative_passages.docid: 6482
negative_passages.text: Why aren't the functions $f(x) = \frac{x-1}{x-1}$ and $f(x) = 1$ the same?
negative_passages.docid: 150642
negative_passages.text: How to prove $\sum^n_{i=1} \frac{1}{i(i+1)} = \frac{n}{n+1}$?
negative_passages.docid: 116722
negative_passages.text: Simplifying $\big(\sum_{i=0}^n\binom{k}{i}\binom{M-k}{n-i}\frac{k-i}{M-n}\big)/{\binom{M}{n}}$