Find the sum to infinity of the following G.P.
(i) `1, (1)/(3) , (1)/(9) . (1)/(27),…`
(ii) ` 2 , (-2)/(3) , (2)/(9) , (-2)/(27),…` .

Explanation

(i) ` a = 1 , r = (1)/(3)`
` therefore S_(oo) = (a)/(1-r) = (1)/(-1(1)/(3)) = (3)/(2)`
(ii) ` a = 2 , r = (-1)/(3)`
` therefore S_(oo) = (a)/(1-r) = (2)/(1 + (1)/(3)) = 2xx (3)/(4) = (3)/(2)` .