Infinite geometric series

Intros
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Lessons
  1. If −1<r<1-1 < r < 1 , an infinite series is convergent:
    S∞= S_{\infty} = t11−r \large\frac{t_1}{1-r}

    Otherwise, an infinite series is divergent:
    S∞= S_{\infty} = undefined
Examples
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Lessons
  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.
    1. 4 + 2 + 1 + …
    2. 2 - 10 + 50 - …
    3. −92 -\frac{9}{2} + 3 - 2 + …
  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.
    1. 0.461‾0.\overline{461}
    2. 5.123‾5.1\overline{23}