Question

Ajutați-ma va rog !!!

Answer 1

Explicație pas cu pas:

1.Metoda verificarii:

n=1;P1:1²=1(1+1)(2+1)/6⇒1=1 adev.

2. n=k

Pk: 1²+2²+3²+...+k²=k(k+1)(2k+1)/6

3.n=k+1

Pk+1: 1²+2²+3²+...+(k+1)²=(k+1)(k+2)(2k+3)/6 ?-trebuie sa o demonstram

1²+2²+3²+...k²+(k+1)²=k(k+1)(2k+1)/6+(k+1)²=[k(k+1)(2k+1)+6(k+1)²]/6=

=[(k+1)(k(2k+1)+6(k+1)]/6=[(k+1)(2k²+k+6k+6)]/6=[(k+1)(2k²+7k+6)]/6=

=[(k+1)(k+2)(2k+3)]/6 deci este adevarat si pentru n=k+1.

Raspuns: Pn adevarat ∀ n∈ N*.

Bafta!