Question

S=3+6+9+.......+936 ​

Answer 1

Dai factor comun pe 3 si aplici suma lui Gauss

S = 3x(1+2+3+.....+312) = 3x[(1+312)x312]/2 = 3x[313x156] = 146484

Answer 2

$S= 3+6+9+...+936 = > S= 3(1+2+3+...+312)\\S= 3\times\frac{312\times313}{2} = > S= 3\times\frac{97656}{2}\\ S= 3\times48828 \\S= 146484$

→ Dam factor comun pe 3, astfel incat sa obtinem in paranteza suma a n numere consecutive.

→ Suma obtinuta in paranteza se calculeaza folosind formula sumei Gauss:

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