Question

Avem x(1)= 3 si x(2)= -1
x(n) = [2 - x(n-1)] / x(n-2)

Calculati
x(1) + x(2) + ... + x(2016)

Answer 1

Răspuns:

-8118432

Explicație pas cu pas:

x₁ = 3 ; x₂ = -1

xₙ = (2-xₙ₋₁)/xₙ₋₂

-----------------

S = x₁+x₂+x₃+.............+x₂₀₁₆ = ?

r = x₂-x₁ = -1-3 = -4

x₃ = x₂+r = -1-4 = -5

x₄ = -5-4 = -9

...................

x₂₀₁₆ = x₁+2015·r = 3 + 2015·(-4) = 3-8060 = -8057

S = 3 + (-1) + (-5) + (-9) +...............+(-8057) =>

S = 3-1-5-9 -..............-8057 = 3 - (1+5+9+.....+8057) = 3-a

a = 1+5+9+.....+8057 = (1+8057)·[(8057-1):4+1]:2 =

= 8058·2015:2 = 4029·2015 = 8118435

S = 3- 8118435 = -8118432