A mega pizza is to be sliced n times, and S n denotes maximum possible number of pieces.
(i) Relation between S n & S n– 1
Text Solution
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(i) (ii)
Sol. Let n lines divides the pizza into S n pieces. Let us add new (n + 1) th line, L which cuts the previous n lines by assumption. Now line L will cut the original pieces into 2 pieces further & we are passing trough (n + 1) such pieces, hence
S n + 1 = S n + (n + 1)
S n = 
+ 1
when S n ≥ 60 where n ∈ N
n(n + 1) + 2 ≥ 60
n 2 + n – 11 ≥ 0
n = 10, is not satisfy
n = 11 is satisfying
⇒ n = 11
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