Question

Calculati: 1+5+9+........+4n-3

Answer 1

Răspuns:

S = n·(2n-1)

Explicație pas cu pas:

S = 1+5+9+........+4n-3 = ?

S = 1+5+9+........+4n-3 = (1+4n-3)·n:2

numarul de termeni = (4n-3-1):4 + 1 = n-1+1 = n

S = (4n-2)·n:2 = 2(2n-1)·n:2

S = (2n-1)·n sau S = n·(2n-1)

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S₁ = 1·(2·1-1) = 1·1 = 1 = a₁ = corect

S₂ = 2·(2·2-1) = 2·3 = 6 = a₁+a₂ = 1+5 = 6 = corect

S₃ = 3·(2·3-1) = 3·5 = 15 = a₁+a₂+a₃ = 1+5+9 = 15 = corect

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