10.5 Infinite geometric series

Infinite geometric series


if 1<r<1-1 < r < 1 , an infinite series is convergent: S= t11r\frac{t_1}{1-r}
Otherwise, an infinite series is divergent: S= undefined
  • 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.
  • 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.
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Infinite geometric series

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