Question

calculati suma:
a)7+13+18+......+6n+1 , oricare n apartine mulțimii numerelor naturale​

Answer 1

Răspuns:

S = n(3n+4)  ; (∀) n ∈ N

Explicație pas cu pas:

a) S = 7 + 13 + 19 + 25 + .......+6n+1

S = (6n+1+7)·[(6n+1-7):6 +1]:2

S = (6n+8)·[(6n-6):6+1]:2

S = (3n+4)·(n-1+1)

S = n(3n+4)

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Verificare :

S₁ = 7 = 1·(3·1+4) = 7

S₂ = 7+13= 20 = 2·(3·2+4) = 2·10 = 20

S₃ = 7+13+19 = 39 = 3·(3·3+4) = 3·13 = 39

S₄ = 7+13+19+25 = 64 = 4·(3·4+4) = 4·16 = 64

S₅ = 7+13+19+25+31 = 95 = 5·(3·5+4) = 5·19 = 95

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