asymptotics and recurrence

Mar 2012
2
0
Let \(\displaystyle n_{0} \in \mathbb{N}, f,s: \mathbb{N} \rightarrow \mathbb{R}\) such that

\(\displaystyle f(n) = f(n-1) + s(n), \forall n \geq n_{0}\)

Prove by induction that if \(\displaystyle s(n) = O(n)\) then \(\displaystyle f(n) = O(n^{2})\)
 
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