query: How to Prove $(-1)^{\frac{1}{2}}$ = i?
positive_passages.docid: 81875
positive_passages.text: why is $\sqrt{-1} = i$ and not $\pm i$?
negative_passages.docid: 100320
negative_passages.text: Prove that $\cos\frac {2\pi}{7}+ \cos\frac {4\pi}{7}+ \cos\frac {8\pi}{7}=-\frac{1}{2}$
negative_passages.docid: 65923
negative_passages.text: How to approach proving $f^{-1}(B\setminus C)=A\setminus f^{-1}(C)$?
negative_passages.docid: 18606
negative_passages.text: How prove $\frac{a^2}{a+2b^2}+\frac{b^2}{b+2c^2}+\frac{c^2}{c+2a^2}\ge 1$
negative_passages.docid: 104828
negative_passages.text: Show that $\cot \frac{\pi}{2m}\cot \frac{2\pi}{2m}\cot \frac{3\pi}{2m}...\cot \frac{(m-1)\pi}{2m}=1$
negative_passages.docid: 73002
negative_passages.text: For $n \geq 2$, prove that $(1- \frac{1}{4})(1- \frac{1}{9})(1- \frac{1}{16})...(1- \frac{1}{n^2}) = \frac{n+1}{2n}$
negative_passages.docid: 118161
negative_passages.text: Proof of dividing fractional expressions
negative_passages.docid: 125701
negative_passages.text: Prove that $-2\log(2) = -2 + \sum_{n=1}^{\infty}\frac{1}{n(2n+1)}$
negative_passages.docid: 87055
negative_passages.text: How to prove $\frac{x}{1+x^2}0$?
negative_passages.docid: 91000
negative_passages.text: Prove that $\frac{1}{a+1}0$
negative_passages.docid: 39908
negative_passages.text: Finding the error in this proof that 1=2
negative_passages.docid: 50599
negative_passages.text: Prove that $\frac{1}{1*3}+\frac{1}{3*5}+\frac{1}{5*7}+...+\frac{1}{(2n-1)(2n+1)}=\frac{n}{2n+1}$
negative_passages.docid: 121544
negative_passages.text: Proof by Induction: $2(\sqrt{n+1} - \sqrt{n}) < \frac{1}{\sqrt{n}} < 2(\sqrt{n}-\sqrt{n-1})$
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: 40348
negative_passages.text: Proving by mathematical induction: $1+\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}+...+\frac{1}{\sqrt{n}}>2(\sqrt{n+1}-1)$
negative_passages.docid: 41645
negative_passages.text: Checking my understanding: $1 - 1 + 1 - 1 + 1 - ... = \frac{1}{2}$
negative_passages.docid: 28332
negative_passages.text: Proof of $\frac{(n-1)S^2}{\sigma^2} \sim \chi^2_{n-1}$