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)

Question

Mathematics

Ann Scott

29 September, 04:43

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)

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Fattykins · Answer 1

Step-by-step 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