Infinite geometric series

Lessons

• Introduction
  If $-1 < r < 1$, an infinite series is convergent:
  $S_{\infty} =$ $\large\frac{t_1}{1-r}$
  
  Otherwise, an infinite series is divergent:
  $S_{\infty} =$ undefined

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• 1.
  Using the common ratio to determine whether a sum to infinity exists
  For each geometric series determine the:
  i) common ratio.
  ii) sum of the first 10 terms.
  iii) sum to infinity.
  
  a)

  4 + 2 + 1 + …
  
  
  b)

  2 - 10 + 50 - …
  
  
  c)

  $-\frac{9}{2}$+ 3 - 2 + …
  
  

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• 2.
  Expressing a repeating decimal as an infinite geometric series
  For the repeating decimal:
  i) express it as an infinite geometric series.
  ii) write it as a fraction by evaluating the sum of the infinite geometric series.
  a)

  $0.\overline{461}$
  
  
  b)

  $5.1\overline{23}$
  
  

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