Benutzer:TommySp/Formeln

Arithmetische Folgen und Reihen

${\displaystyle a_{n}=a_{1}+(n-1)\cdot d}${\displaystyle a_{n}=a_{1}+(n-1)\cdot d}

${\displaystyle {\begin{aligned}s_{n}&={\frac {(a_{1}+a_{n})\cdot n}{2}}\\&={\frac {n\cdot \lbrack 2a_{1}+(n-1)\cdot d\rbrack }{2}}\end{aligned}}}${\displaystyle {\begin{aligned}s_{n}&={\frac {(a_{1}+a_{n})\cdot n}{2}}\\&={\frac {n\cdot \lbrack 2a_{1}+(n-1)\cdot d\rbrack }{2}}\end{aligned}}}

Geometrische Folgen und Reihen

${\displaystyle a_{n}=a_{1}\cdot q^{n-1}}${\displaystyle a_{n}=a_{1}\cdot q^{n-1}}

${\displaystyle s_{n}=a_{1}\cdot {\frac {1-q^{n}}{1-q}}}${\displaystyle s_{n}=a_{1}\cdot {\frac {1-q^{n}}{1-q}}}

${\displaystyle s=\lim _{n\to \infty }s_{n}={\frac {a_{1}}{1-q}}}${\displaystyle s=\lim _{n\to \infty }s_{n}={\frac {a_{1}}{1-q}}}