How to prove f(n)=O(n) for any integer ⩾1, if f(1)=1 and f(n)=2f(⌊n/2⌋)+1 for n⩾2? Do you...

How to prove f(n)=O(n) for any integer ⩾1, if f(1)=1 and f(n)=2f(⌊n/2⌋)+1 for n⩾2?

Do you need induction? If so, how do you do it?

Expert Solution

Dear Learner,

The solution to your question is in the attached photos. Please refer to them for the same

We have used the method of induction for the proof

I hope I have explained the question the way you were expecting. If you still have any doubts or want any further explanation, feel free to ask us in the comment section.

Please leave a like if this was helpful.

Thanks,

Happy Studying.

venereology answered 6 months ago

If f(n) = 3n+2 and g(n) = n, then Prove that f(n) = O (g(n))

Prove that τ(n) < 2 n for any positive integer n. This is a question in...

Prove that τ(n) < 2 n for any positive integer n. This is a question in Number theory

1.)Prove that f(n) = O(g(n)), given: F(n) = 2n + 10; g(n) = n 2.)Show that...

1.)Prove that f(n) = O(g(n)), given: F(n) = 2n + 10; g(n) = n 2.)Show that 5n2 – 15n + 100 is Θ(n2 ) 3.)Is 5n2 O(n)?

Let F be a finite field. Prove that there exists an integer n≥1, such that n.1_F...

Let F be a finite field. Prove that there exists an integer n≥1, such that n.1_F = 0_F . Show further that the smallest positive integer with this property is a prime number.

Prove that if n is an integer and n^2 is even the n is even.

Prove why f(n)=big omega(g(n)) then f(n)=o(g(n)) is NEVER TRUE. Prove why f(n) +g(n) =Theta(max(f(n),g(n)) is ALWAYS...

Prove why f(n)=big omega(g(n)) then f(n)=o(g(n)) is NEVER TRUE. Prove why f(n) +g(n) =Theta(max(f(n),g(n)) is ALWAYS TRUE

Use induction to prove that for any positive integer n, 8^n - 3^n is a multiple...

Use induction to prove that for any positive integer n, 8^n - 3^n is a multiple of 5.

Prove the following theorem. If n is a positive integer such that n ≡ 2 (mod...

Prove the following theorem. If n is a positive integer such that n ≡ 2 (mod 4) or n ≡ 3 (mod 4), then n is not a perfect square.

For f: N x N -> N defined by f(m,n) = 2m-1(2n-1) a) Prove: f is...

For f: N x N -> N defined by f(m,n) = 2m-1(2n-1) a) Prove: f is 1-to-1 b) Prove: f is onto c) Prove {1, 2} x N is countable

Prove that for any integer n the expression n7/7 + n5/5 + 23n/35 is whole integer....

Prove that for any integer n the expression n7/7 + n5/5 + 23n/35 is whole integer. (Hint: Note that the problem can be state in a following equivalent form: 35 | (5n7 +7n5 +23n); even further, by the previews theorem, it would be enough to show that (5n7 + 7n5 + 23n) is divisible by 5 and 7.)

Question