Find the sum of the following series ,
` (i) 0.5 + 0.05 + 0.005 + 0.0005+…`
(ii) ` 0.3 + 0.18 + 0.108 + … `

Explanation

(i) ` a = 0.5 , r = (1)/(10)`
` therefore S_(oo) = (a)/(1-r) = (0.5)/(1 - (1)/(10)) = (5)/(10) xx (10)/(9) = (5)/(9)`
(ii) ` a = 0.3 , r = 0.6 `
` therefore S_(oo) = (a)/(1-r) = (0.3)/(1 - 0.6) = (0.3)/(0.4) = (3)/(4)` .