Question

cum se rezolva suma 1*2+2*3+3*4+................n*(n+1)

Answer 1

Răspuns:

S=n(n+1)(n+2)/6

Explicație pas cu pas:

$1*2+2*3+3*4+...+n*(n+1)=1+1^2+2+2^2+3+3^2+...+n+n^2=\\=(1+2+3+...+n)+(1^2+2^2+3^2+...+n^2)=\frac{n(n+1)}{2} +\frac{n(n+1)(2n+1)}{6} =\\=\frac{n(n+1)}{2} *(1+\frac{2n+1}{3})= \frac{n(n+1)}{2} *\frac{2n+4}{3}=\\=\frac{n(n+1)(n+2)}{6}$