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#mimetex(0.999...=0.\dot{9})
#mimetex(\frac{1}{3}\quad\quad\quad=0.\dot{3})
#mimetex(\frac{1}{3} * 3=0.\dot{3} * 3)
#mimetex(1\quad\quad\quad=0.\dot{9})
#mimetex(1-0.\dot{9}=0.\dot{0})
#mimetex(0.\dot{0} = 0)
#mimetex(0.\dot{9})
#mimetex(a_1=0.9)
#mimetex(r=0.1)
#mimetex(a_1r^{n-1})
#mimetex(S_n=\frac{a_1(r^n-1)}{r-1})
#mimetex(S_n=\frac{a_1(r^n-1)}{r-1}=\frac{0.9(0.1^n-1)}{-0.9})
#mimetex(n)
#mimetex(0.\dot{9}=\lim_{n\to\infty}S_n=\lim_{n\to\infty}\frac{0.9(0.1^n-1)}{-0.9}=\lim_{n\to\infty}-(0.1^n-1)=\lim_{n\to\infty}1-0.1^n=1)
#mimetex(0.\dot{9})
#mimetex(p\(1\)=\frac{99}{100})
#mimetex(p\(2\)=\frac{1}{100})
#mimetex(p\(3\)=\frac{1}{100}+\frac{1}{100}\cdot\frac{1}{99})
#mimetex(p\(3\)=\frac{1}{100}+\frac{1}{100}\cdot\frac{1}{99}=\frac{1}{100}\(1+\frac{1}{99}\)=\frac{1}{100}\(\frac{99}{99}+\frac{1}{99}\)=\frac{1}{100}\cdot\frac{100}{99}=\frac{1}{99})
#mimetex(p\(4\)=\frac{1}{100}+\frac{1}{100}\cdot\frac{1}{99}+\frac{1}{100}\cdot\frac{1}{98}+\frac{1}{100}\cdot\frac{1}{99}\cdot\frac{1}{98})
#mimetex(p\(3\)=\frac{1}{100}+\frac{1}{100}\cdot\frac{1}{99})
#mimetex(=\frac{1}{99})
#mimetex(p\(4\)=\frac{1}{100}+\frac{1}{100}\cdot\frac{1}{99}+\frac{1}{100}\cdot\frac{1}{98}+\frac{1}{100}\cdot\frac{1}{99}\cdot\frac{1}{98}=\frac{1}{99}+\frac{1}{99}\cdot\frac{1}{98})
#mimetex(=\frac{1}{99}\(1+\frac{1}{98}\)=\frac{1}{99}\cdot\frac{99}{98}=\frac{1}{98})
#mimetex(p\(n\)=\frac{1}{102-n})
#mimetex(p\(n\)=p\(n-1\)+p\(n-1\)\cdot\frac{1}{102-n})
#mimetex(p\(n\)=\frac{1}{102-n})
#mimetex(p\(n\)=p\(n-1\)+p\(n-1\)\cdot\frac{1}{102-n})
#mimetex(p\(2\)=\frac{1}{100})
#mimetex(p\(3\)=p\(2\)+p\(2\)\cdot\frac{1}{102-3}=\frac{1}{100}+\frac{1}{100}\cdot\frac{1}{99}=\frac{1}{99}=\frac{1}{102-n})
#mimetex(p\(n+1\)=p\(n\)+p\(n\)\cdot\frac{1}{102-\(n+1\)}=\frac{1}{102-n}+\frac{1}{102-n}\cdot\frac{1}{102-\(n+1\)}=\frac{1}{102-n}\(1+\frac{1}{102-n-1}\))
#mimetex(=\frac{1}{102-n}\(\frac{102-n-1}{102-n-1}+\frac{1}{102-n-1}\)=\frac{1}{102-n}\(\frac{102-n}{102-n-1}\)=\frac{1}{102-\(n+1\)})
#mimetex(p\(100\)=\frac{1}{102-100}=\frac{1}{2})
#mimetex(p\(n\))
#mimetex(p\(1\)=1)
#mimetex(p\(2\)=\frac{365}{365}\cdot\frac{364}{365})
#mimetex(p\(3\)=\frac{365}{365}\cdot\frac{364}{365}\cdot\frac{363}{365})
#mimetex(p\(n\)=\prod_{i=1}^{n}\frac{366-i}{365}=\frac{1}{365^n}\cdot\frac{365!}{(365-n)!})
#mimetex(1-\frac{1}{365^n}\cdot\frac{365!}{(365-n)!})
#mimetex(\frac{1}{4})
#mimetex(p\(n\))
#mimetex(f\(n\))
#mimetex(1-p=\(1-w^n\)^k);を書き換えて&mimetex(k = \frac{\log(1-p)}{\log(1-w^n)})
#mimetex(\frac{\partial \bf{P}}{\partial \bf{t}})
#mimetex( -\frac{b \pm \sqrt{b^2-4ac}}{2a})
#mimetex( e^{i \pi} + 1 = \cos (\pi) + i\sin(\pi) + 1 = 0 )
#mimetex(D=(\bf{x} - \bf{\mu})^\top \Sigma^{-1} (\bf{x} - \bf{\mu}))


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