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})