Problem 1 Show that f(n) = 1² + 2² + 3² + . . . + n² is O(n³) Problem 2 Define H(n) = 1+1/2+1/3+.. (a) H(2k) ≥ 1+k/2_ \k

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Problem 1 Show That F N 1 2 3 N Is O N Problem 2 Define H N 1 1 2 1 3 A H 2k 1 K 2 K 1 (125.78 KiB) Viewed 23 times

Problem 1 Show that f(n) = 1² + 2² + 3² + . . . + n² is O(n³) Problem 2 Define H(n) = 1+1/2+1/3+.. (a) H(2k) ≥ 1+k/2_ \k≥1 (b) H(2k) ≤1+k_ \k≥1 (c) use (a) and (b) to argue that H(n) = O(log n) + 1/n. Prove by induction that: 4 6 2 2 2