Question

Use the definition of O (f) to show that 4^n + 25 is O (5^n) (ii) show that 5^n is not O (4^n)

Answer 1

Explanation:

i) if O (5^n)= 4^n + 25

O (f) should be = (20^n)/f + 25

Then

O(5^n)= (20^n)/(5^n) + 25 = (20/5)^n +25=4^n+25

ii) O (4^n)=(20^n)/(4^n) + 25 = (20/4)^n +25=5^n+25

And 5^n+25 is not = 5^n