Question

a) Calculați
1/2 la n-1 - 1/ 2 la n

b) Folosind rezultatul de la punctul a), calculati: 1/2-(1/2*2+1/2*3+1/2*4+…+1/2*10)

Dau coroana

Answer 1

Răspuns:

Explicație pas cu pas:

a)

1/2^n-1 - 1/2^n = 2/2^n - 1/2^n = 1/2^n

b)

1/2^2 = 1/2 - 1/2^2

1/2^3 = 1/2^2 - 1/2^3

1/2^4 = 1/2^3 - 1/2^4

.......

1/2^10 = 1/2^9 - 1/2^10

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1/2^2 + 1/2^3 + 1/2^4 + ...+ 1/2^10 = 1/2 - 1/2^2 + 1/2^2 - 1/2^3 + 1/2^3 - 1/2^4

+ 1/2^9 - 1/2^10 = 1/2 - 1/2^10

________________

1/2 - (1/2 - 1/2^10) = 1/2 - 1/2 + 1/2^10 = 1/2^10