Question

Calculati , folosind factorul comun
3+6+9+....+90

Answer 1

3(1+2+3+...+30)= 3* 30*31 :2 = 90*31:2=45*31=1395

Answer 2

Vom folosi formula sumei lui Gauss:

$1+2+3+...+n=\frac{n(n+1)}{2}$

[tex]S=3+6+9+...+90\\ S=3\cdot1+3\cdot2+3\cdot3+...+3\cdot30\\ S=3(1+2+3+...+30)\\ S=3\cdot\frac{30\cdot31}{2}=\boxed{1395}[/tex]