A recurring decimal is given by

MATHEMATICS · Multi-part · A Level · Mathematics · Sequences and series · Sequences and series

Problem

0.\overline{135}=0.135135135\dots

(i) Express this decimal as an infinite geometric series. (ii) Hence, write it in the form

\dfrac{p}{q}

, where

p

and

q

are positive integers with no common factor other than

1