Zurück zu Identitäten
(nk)+(nk−1)=n!k!⋅(n−k)!+n!(k−1)!⋅(n−k+1)!{\displaystyle {n \choose k}+{n \choose k-1}={\frac {n!}{k!\cdot (n-k)!}}+{\frac {n!}{(k-1)!\cdot (n-k+1)!}}} =n!⋅(n+1−k)k!⋅(n+1−k)!+n!⋅kk!⋅(n−k+1)!=(n+1)!k!⋅(n+1−k)!=(n+1k){\displaystyle ={\frac {n!\cdot (n+1-k)}{k!\cdot (n+1-k)!}}+{\frac {n!\cdot k}{k!\cdot (n-k+1)!}}={\frac {(n+1)!}{k!\cdot (n+1-k)!}}={n+1 \choose k}}