Arithmetische Folgen und Reihen
a n = a 1 + ( n − 1 ) ⋅ d {\displaystyle a_{n}=a_{1}+(n-1)\cdot d}
s n = ( a 1 + a n ) ⋅ n 2 = n ⋅ [ 2 a 1 + ( n − 1 ) ⋅ d ] 2 {\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
a n = a 1 ⋅ q n − 1 {\displaystyle a_{n}=a_{1}\cdot q^{n-1}}
s n = a 1 ⋅ 1 − q n 1 − q {\displaystyle s_{n}=a_{1}\cdot {\frac {1-q^{n}}{1-q}}}
s = lim n → ∞ s n = a 1 1 − q {\displaystyle s=\lim _{n\to \infty }s_{n}={\frac {a_{1}}{1-q}}}
