$$1+1=2$$ $$2>1$$ $$\gt \geqq = \ne \leqq \lt$$ $$2\cdot3^4$$ $$2\cdot3^{n-1}$$ $${1 \over 2}*2=1$$ $$\frac{1+2}{2}*2=3$$ $$\sqrt{2^2} = 2$$ $$\sqrt[3]8 = 2$$ $$\log_2 8 = 3$$ $$\therefore y=x+1$$ $$\mathbf{sin}2{\theta}=2\mathbf{sin}{\theta}\,\mathbf{cos}{\theta}$$ $$\sin^{2} \theta + \cos^{2} \theta = 1$$ $$\mathbf{sin}(\alpha+\beta)=\mathbf{sin}{\alpha}\,\mathbf{cos}{\beta}+\mathbf{cos}{\alpha}\,\mathbf{sin}{\beta}$$ $$a_n=a+(n-1)d$$ $$s_n=\frac{1}{2}n(a_1+a_n)=\frac{1}{2}n \{ 2a+(n-1)d \}$$ $$\sum_{k=1}^n k^2 = 1^2+2^2+3^3+\dots+n^2=\frac{n(n+1)(2n+1)}{6}$$ $$\sum_{n=1}^\infty ar^{n-1}=a+ar+ar^2+\dots = \begin{eqnarray} \left\{ \begin{array}{l} \dfrac{a}{1-r}&(|r|\lt1)\\ 発散&(|r|\geqq1) \end{array} \right. \end{eqnarray} (a\ne0)$$ $$ \begin{pmatrix} a & b\cr c & d \end{pmatrix} \begin{pmatrix} 1 & 0\cr 0 & 1 \end{pmatrix} = \begin{pmatrix} a & b\cr c & d \end{pmatrix} $$ $$f'(x)=\lim_{h\to 0}\frac{f(x+h)-f(x)}{h}$$ $$f'(x) = \lim_{ \Delta x \to 0 } \frac{ f(x + \Delta x) - f(x) }{ \Delta x }$$ $$\int_a^b f(x)dx= \left[ F(x) \right]_{a}^{b}=F(b)-F(a) $$ $$e^{i\pi} = -1$$