F.6 MATHS

(a)(i) 1/4
(ii) 1/4 * 1/4 = 1/16
(iii) (1/4)^n = 1/4^n = 1/[2^(2n)]
(b) Portion of cake P will get after dividing n times
= 1/4 + (1/4)^2 + (1/4)^3 + ... + (1/4)^n
= (1/4)[1 - (1/4)^n] / (1 - 1/4)
= (1/3)[1 - (1/4)^n]
As n -> ∞, (1/4)^n -> ∞ => (1/3)[1 - (1/4)^∞] = 1/3
After infinite number of division, P will get a total of 1/3 of the original cake.