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2 (25 pts). Let an algorithm has complexity S(n)=S(n1)+f(n), where for k=1,2,3, f(k)=k2+k/3. Answer these two questions: (1) Find the closed form for S(n) if

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2 (25 pts). Let an algorithm has complexity S(n)=S(n1)+f(n), where for k=1,2,3, f(k)=k2+k/3. Answer these two questions: (1) Find the closed form for S(n) if S(2)=1. (2) Prove by mathematical induction that the closed form you found is correct

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