Luokka:Matematiikka

Luokka:Matematiikka

85-;+98.58=[math]\displaystyle{ \sum_{n=0}^\infty \frac{x^n}{n!} }[/math]/∞√89!523 ‰(≤783=980.65Y[67∂]ax2 + bx + c = 0 [math]\displaystyle{ ax^2 + bx + c = 0 }[/math][math]\displaystyle{ ax^2 + bx + c = 0\, }[/math] [math]\displaystyle{ x_{1,2}=\frac{-b\pm\sqrt{b^2-4ac}}{2a} }[/math][math]\displaystyle{ 2 = \left( \frac{\left(3-x\right) \times 2}{3-x} \right) }[/math][math]\displaystyle{ S_{new} = S_{old} + \frac{ \left( 5-T \right) ^2} {2} }[/math][math]\displaystyle{ \int_a^x \int_a^s f(y)\,dy\,ds = \int_a^x f(y)(x-y)\,dy }[/math][math]\displaystyle{ \sum_{m=1}^\infty\sum_{n=1}^\infty\frac{m^2\,n} {3^m\left(m\,3^n+n\,3^m\right)} }[/math][math]\displaystyle{ u'' + p(x)u' + q(x)u=f(x),\quad x\gt a }[/math] [math]\displaystyle{ |\bar{z}| = |z|, |(\bar{z})^n| = |z|^n, \arg(z^n) = n \arg(z)\, }[/math][math]\displaystyle{ \lim_{z\rightarrow z_0} f(z)=f(z_0)\, }[/math][math]\displaystyle{ \phi_n(\kappa) = \frac{1}{4\pi^2\kappa^2} \int_0^\infty \frac{\sin(\kappa R)}{\kappa R} \frac{\partial}{\partial R}\left[R^2\frac{\partial D_n(R)}{\partial R}\right]\,dR }[/math][math]\displaystyle{ \phi_n(\kappa) = 0.033C_n^2\kappa^{-11/3},\quad \frac{1}{L_0}\ll\kappa\ll\frac{1}{l_0}\, }[/math][math]\displaystyle{ f(x) = \begin{cases}1 & -1 \le x \lt 0 \\ \frac{1}{2} & x = 0 \\ 1 - x^2 & 0 \lt x\le 1\end{cases} }[/math][math]\displaystyle{ {}_pF_q(a_1,...,a_p;c_1,...,c_q;z) = \sum_{n=0}^\infty \frac{(a_1)_n\cdot\cdot\cdot(a_p)_n}{(c_1)_n\cdot\cdot\cdot(c_q)_n}\frac{z^n}{n!}\, }[/math]

Leibnizin sarja
[math]\displaystyle{ \frac{\pi}{4} = \sum_{k=0}^\infty \frac{(-1)^k}{2k+1} }[/math]

Eulerin sarja
[math]\displaystyle{ \frac{\pi^2}{6} = \sum_{k=1}^\infty \frac{1}{k^2} }[/math]

Samankaltainen sarja
[math]\displaystyle{ \frac{\pi^2}{8} = \sum_{k=0}^\infty \frac{1}{(2k+1)^2} }[/math]

Erilainen sarja
[math]\displaystyle{ \frac{4}{\pi} = 1 + \frac{1}{3 + \frac{4}{5 + \frac{9}{7 + \frac{16}{9 + \frac{25}{11 + \frac{36}{13 + ...}}}}}} }[/math]

Wallisin tulonlähde

[math]\displaystyle{ \frac{2}{1} \cdot \frac{2}{3} \cdot \frac{4}{3} \cdot \frac{4}{5} \cdot \frac{6}{5} \cdot \frac{6}{7} \cdot \frac{8}{7} \cdot \frac{8}{9} \cdots = \frac{\pi}{2} }[/math]

Joka voidaan kirjoittaa myös näin:

[math]\displaystyle{ \prod_{n=1}^{\infty} \frac{(2n)^2}{(2n)^2-1} = \prod_{n=1}^{\infty} \frac{2n}{2n-1} \cdot \frac{2n}{2n+1} = \frac{\pi}{2} }[/math]

• 1+1=11
• 6-5=1
• 7 + 7 = 12
• 14 + 14 - 14 x 14 : 14 = 14,14141411414141414...
• π=3