Chapter 1 Text work review

1.

4. Does 0.9999... = 1?

0.9999.... = 0.9 + 0.09 + 0.009 + ...

t₁ = \( \frac{9}{10} \) , r = \( \frac{1}{10} \)

S\( _\infty \) = \( \frac{ \frac{9}{10} }{1 - \frac{1}{10} } = \frac{ \frac{9}{10} }{ \frac{9}{10} } = 1 \)