Question

Calculati 3+6+9+12+......+300

Answer 1

Dam factor 3 si obtinem 3(1+2+3+4+...+100).

Pt. suma din paranteza aplicam formula sumei lui Gauss : $\frac{n(n+1)}{2}$, unde n reprezinta nr de termeni.

=> 1+2+3+...+100 = $\frac{100(100+1)}{2}=\frac{100*101}{2}=50*101=5050$

3+6+9+...+300 = 3(1+2+3+...+100) = 3*5050 = 15 150 (acesta este rezultatul sumei date)