Question

Există vreo formulă prin care pot rezolva asta : S=1*2+2*3+3*4+...+n*(n+1) ???

Answer 1

S=1•2+2•3+3•4+....n(n+1)

S=1(1+1)+2(2+1)+3(3+1)+4(4+1)+....+n(n+1)

S= 1+2+3+4+....+n + 1²+2²+3²+4²+....+n²

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

S=[3n(n+1)+ n(n+1)(2n+1)]/6

S=n(n+1)(3+2n+1)/6

S=n(n+1)(2n+4)/6

S=n(n+1)(n+2)/3