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What is the sum of the first five terms of a geometric series with a1 = 10 and r = 1/5? Express your answer as an improper fraction in lowest terms without using spaces.

Respuesta :

sqdancefan
Using the formula for the sum,
  Sn = a₀×(rⁿ -1)/(r -1)
you have
  S₅ = 10×((1/5)⁵ -1)/(1/5 -1)
  = 10×(-3124/3125)/(-4/5)
  = 10×781/625

  S₅ = 1562/125

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Or, you can add up the terms
  10 + 2 + 2/5 + 2/25 + 2/125 = (1250 +250 +50 +10 +2)/125
  = 1562/125