Sequences and Series

Hong Kong

Stage 4 - Stage 5

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

4min

The decimal $0.6666$0.6666$...$... can be expressed as a fraction.

Easy

1min

The recurring decimal $0.444444\dots$0.444444… can be expressed as a fraction when viewed as an infinite geometric series.

Easy

3min

Consider the number $0.252525$0.252525$\ldots$…

Easy

1min

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