3 + 6 + 9 + ...... + 123 =
= 3 × ( 1 + 2 + 3 + ..... + 41 ) ← am dat factor comun pe 3
S = 1 + 2 + 3 + .... + 41
→ aplic formula sumei lui Gauss:
S = 41 termeni × ( 1 + 41 ) : 2
↓
suma dintre primul termen si ultimul termen al sumei
= 3 × 41 × ( 1 + 41 ) : 2
= 123 × 42 : 2 =
= 123 × 21
= 2 583
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