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Question
Find the sum of the following geometric series:
0.15 + 0.015 + 0.0015 + ... to 8 terms;
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Solution
Here, a = 0.15 and r \[= \frac{a_2}{a_1} = \frac{0 . 015}{0 . 15} = \frac{1}{10}\] .
\[S_8 = a\left( \frac{1 - r^8}{1 - r} \right) \]
\[ = 0 . 15\left( \frac{1 - \left( \frac{1}{10} \right)^8}{1 - \frac{1}{10}} \right)\]
\[ = 0 . 15\left( \frac{1 - \frac{1}{{10}^8}}{\frac{1}{10}} \right)\]
\[ = \frac{1}{6}\left( 1 - \frac{1}{{10}^8} \right)\]
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