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kirill115 [55]
3 years ago
10

The sum of infinity of the series 2/3 – 4/3² + 2/3³ + 4/3⁴ is​

Mathematics
2 answers:
Levart [38]3 years ago
8 0

Answer:

  • 7/20

Step-by-step explanation:

<u>It seems there are two patterns in the series:</u>

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

<u>Using sum of infinity of the geometric series formula:</u>

  • S∞ = a₁/(1 - r)

<u>Applying this to both patterns:</u>

  • 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

<u>Sum of the two results:</u>

  • 3/4 + (-2/5) =
  • 5/5*3/4 - 4/4*2/5 =
  • 15/20 - 8/20 =
  • 7/20
Brut [27]3 years ago
6 0

Answer:

\frac{3}{4}  -  \frac{2}{4}  =  \frac{1}{4}

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