Respuesta :

DarrallCharityjapan

Answer:

[tex] \frac{3}{4} - \frac{2}{4} = \frac{1}{4} [/tex]

mhanifa

Answer:

  • 7/20

Step-by-step explanation:

It seems there are two patterns in the series:

  • 2/3, 2/3³, ... with a₁ = 2/3 and r = 1/9
  • - 4/3², 4/3⁴, ... with a₁ = -4/9 and r = -1/9

Using sum of infinity of the geometric series formula:

  • S∞ = a₁/(1 - r)

Applying this to both patterns:

  • S₁ = 2/3÷(1 - 1/9) = 2/3 ÷ 8/9 = 2/3×9/8 = 3/4
  • S₂ = -4/9÷(1 - (-1/9)) = -4/9÷10/9 = -4/9×9/10 = - 2/5

Sum of the two results:

  • 3/4 + (-2/5) =
  • 5/5*3/4 - 4/4*2/5 =
  • 15/20 - 8/20 =
  • 7/20

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