Question

Calculati urmatoarele sume 2+3+4+....+30,9+10+11+....+30

Answer 1

S = 2 + 3 + 4 + ..... + 30

→ stabilesc cati termeni are suma cu ratia 1

30 - 2 + 1 = 28 + 1 = 29

→ aplic formula sumei lui Gauss:

S = 29 × ( 2 + 30 ) / 2

S = 29 × 32 / 2

S = 29 × 16

S = 464

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S = 9 + 10 + 11 + ....... + 30

S = ( 30 - 9 + 1 ) termeni ×  ( 9 + 30 ) / 2

S = 22 × 39 / 2

S = 11 × 39

S = 429