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Find the sum to infinity of the following series. 0.5 + 0.05 + 0.005 +…

Find the sum to infinity of the following series. 0.5 + 0.05 + 0.005 + 0.0005 + …..
  • A.
    (frac{5}{8})
  • B.
    (frac{5}{7})
  • C.
    (frac{5}{11})
  • D.
    (frac{5}{9})
Correct Answer: Option 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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