Prove or disprove that 7n=O(5n) + 7.

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Prove or disprove that 7n=O(5n) + 7.

Prove or disprove that 7ⁿ=O(5ⁿ) + 7.

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Answer 1

Answer #1

7n = O(5n) + 7
=> 7n - 7 = O(5n)
if f(n) = O(g(n)) then f(n) <= cg(n) for all n>=n0

Assume 7n - 7 = O(5n) is True
Then we need to find a c>0 and n0 for which (7n-7) <= c(5n)
Let c = 7/5 (>0)
Then (7/5)*5n = 7n
and 7n > (7n-7) for all n>=0

Here Our Assumption is True.
Therefore 7n=O(5n) + 7 is True

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Answer 2

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