Sequences and Series

The recurring decimal $0.8888\dots$0.8888… can be expressed as a fraction when viewed as an infinite geometric series.

a

Express the first decimal place, $0.8$0.8 as an unsimplified fraction.

b

Express the second decimal place, $0.08$0.08 as an unsimplified fraction.

c

Hence write, using fractions, the first five terms of the geometric sequence representing $0.8888\dots$0.8888…

d

State the values of $a$`a`, the first term, and $r$`r`, the common ratio, of this sequence.

$a$`a`$=$=$\editable{}$

$r$`r`$=$=$\editable{}$

e

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.

Easy

Approx 4 minutes

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Use arithmetic and geometric sequences and series

Apply sequences and series in solving problems