Explain why is an infinite geometric series.

MATHEMATICS · Multi-part · CBSE · Mathematics · Sequences and Series · Sequences and Series

Problem

1. Explain why

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

is an infinite geometric series. (1) Explain why

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

is an infinite geometric series. (2) Hence show that

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