Hier experiementiere ich ein wenig mit der TeX funktion von Wikipedia.
sn = n*[2a1 + (n-1)*d]/2
s n = n ⋅ [ 2 a 1 + ( n − 1 ) ⋅ d ] 2 {\displaystyle s_{n}={\frac {n\cdot \lbrack 2a_{1}+(n-1)\cdot d\rbrack }{2}}}
an = a1 + (n-1)d
a n = a 1 + ( n − 1 ) ⋅ d {\displaystyle a_{n}=a_{1}+(n-1)\cdot d}
Arithmetische Folgen und Reihen
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}}}
Sonstiges
Z = R 1 + X L 1 + X L 2 ⋅ ( R 2 + X C ) X L 2 + R 2 + X C = R 1 + j ω L 1 + j ω L 2 R 2 + L 2 C j ω L 2 + R 2 + 1 j ω C = 10 + 10 j {\displaystyle Z=R_{1}+X_{L_{1}}+{\frac {X_{L_{2}}\cdot (R_{2}+X_{C})}{X_{L_{2}}+R_{2}+X_{C}}}=R_{1}+j\omega L_{1}+{\frac {j\omega L_{2}R_{2}+{\frac {L_{2}}{C}}}{j\omega L_{2}+R_{2}+{\frac {1}{j\omega C}}}}=10+10j}
