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Induction. Consider the following recurrence definition: T(1) = 1, T(i+1) = T(i) + 3i² +3¡ +1. a. Prove by induction the predicate p(i) = ( T(i) = ¡³ ) h. Give the Big Oh() attribute of the following algorithm as a function of N:

Induction. Consider the following recurrence definition: T(1) = 1, T(i+1) = T(i) + 3i² +3¡ +1. a. Prove by induction the predicate p(i) = ( T(i) = ¡³ ) h. Give the Big Oh() attribute of the following algorithm as a function of N:

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Induction. Consider the following recurrence definition: T(1) = 1, T(i+1) = T(i) + 3i² +3¡ +1. a. Prove by induction the predicate p(i) = ( T(i) = ¡³ ) b. Give the Big Oh() attribute of the following algorithm as a function of N: int T, i; T=1; i=1; while (T<=N) {T=T+3*i*i+3*i+1; i=i+1;}
Transcribed Image Text:Induction. Consider the following recurrence definition: T(1) = 1, T(i+1) = T(i) + 3i² +3¡ +1. a. Prove by induction the predicate p(i) = ( T(i) = ¡³ ) b. Give the Big Oh() attribute of the following algorithm as a function of N: int T, i; T=1; i=1; while (T<=N) {T=T+3*i*i+3*i+1; i=i+1;}
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