A Explain why is an infinite geometric series.

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

Problem

1. a Explain why

0.\overline{3} = \frac{3}{10} + \frac{3}{100} + \frac{3}{1000} + \dots

is an infinite geometric series. (a) Explain why

0.\overline{3} = \frac{3}{10} + \frac{3}{100} + \frac{3}{1000} + \dots

is an infinite geometric series. (b) Hence show that

0.\overline{3} = \frac{1}{3}