The recurring decimal $0.8888\dots$0.8888… can be expressed as a fraction when viewed as an infinite geometric series.
Express the first decimal place, $0.8$0.8 as an unsimplified fraction.
Express the second decimal place, $0.08$0.08 as an unsimplified fraction.
Hence write, using fractions, the first five terms of the geometric sequence representing $0.8888\dots$0.8888…
State the values of $a$a, the first term, and $r$r, the common ratio, of this sequence.
If we add up infinitely many terms of this sequence, we will have the fraction equivalent of our recurring decimal. Calculate the infinite sum of the sequence as a fraction.
Use arithmetic and geometric sequences and series
Apply sequences and series in solving problems