NEAT HANDWRITING ONLY PLEASE!!
SHOW EVERY SINGLE STEP:)
Prove the following claims. For parts (a)-(f), use either thedefinitions (of Big-O, Big-Ω, or Big-Θ) or a limit argument. Forpart (g), use the definition of Big-Ω and induction.
(a.) 2n ∈ O(n!)
(b.) log2(n) ∈ O(n/ log2(n))
(c.) log2(n2) +log2(100n10) ∈ O(log2(n))
(d.) n1/2 ∈ O(n2/3)
(e.) log3(n) ∈ Θ(log2(n))
(f.) 2n ∈ O(3n/n2)
(g.) Recall that the Fibonacci sequence is defined recursivelyas F0 = 0,F1 = 1, and Fn=Fn-1 + Fn-2 for n ≥ 2. Prove that
Fn ∈ Ω((√2)n)
Answer
Answer
OR
OR