slothlikesky slothlikesky
  • 24-07-2022
  • Mathematics
contestada

For the geometric series 1 - 2/3 + 4/9 - 8/27....
find s8

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jeremiahjojygeorge jeremiahjojygeorge
  • 24-07-2022

Answer:

Step-by-step explanation:

The sum of an alternating geometric series SUM((-1)^n*ar^n) = a/(1+r). The given series has r=2/3 and a=1. The sum will be 1/(1+2/3)= 3/5

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skabetix skabetix
  • 24-07-2022

Hello,

We have s0 = 1 and q = -2/3

[tex]S _{n} = S _{0} \times q {}^{n} = 1 \times ( - \frac{2}{3} ) {}^{n} [/tex]

[tex]S _{8} = ( - \frac{2}{3} ) {}^{8} = \frac{2 {}^{8} }{3 {}^{8} } = \frac{256}{6 561} [/tex]

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