MisterZeng
MisterZeng MisterZeng
  • 23-03-2022
  • Mathematics
contestada

Find the sum of the geometric series 128 - 64 + 32 – ... - 1.

Find the sum of the geometric series 128 64 32 1 class=

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reinhard10158
reinhard10158 reinhard10158
  • 23-03-2022

Step-by-step explanation:

this sequence has 8 terms and the common ratio or multiplication factor is -1/2.

we could add these 8 numbers manually or use the formula :

Sn = a1(1 - r^n)/(1 - n)

when r < 1 (like in our case -1/2).

S8 = 128(1 - (-1/2)⁸)/(1 - -1/2) =

= 128(1 - 1/256)/(3/2) = (128×255/256)/(3/2) =

= (255/2)/(3/2) = 255/2 × 2/3 = 255/3 = 85

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