Find the sum to infinity of the following series. 0.5 + 0.05 + 0.005 + 0.0005 + …..
- \(\frac{5}{8}\)
- \(\frac{5}{7}\)
- \(\frac{5}{11}\)
-
\(\frac{5}{9}\)
The correct answer is: D
Explanation
Using S\(\infty\) = \(\frac{a}{1 - r}\)
r = \(\frac{0.05}{0.5}\) = \(\frac{1}{10}\)
S\(\infty\) = \(\frac{0.5}{{\frac{1}{10}}}\)
= \(\frac{0.5}{({\frac{9}{10}})}\)
= \(\frac{0.5 \times 10}{9}\)
= \(\frac{5}{9}\)
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