17.4 Infinite geometric series
Infinite geometric series
Basic concepts:
 Arithmetic series
 Geometric sequences
 Geometric series
Lessons
Notes:
if $1 < r < 1$, an infinite series is convergent: S_{ ∞}= $\frac{t_1}{1r}$
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.