algorithm - Giving a simple function so that sum S(n) is O(f(n))? -

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Stuck on for some time

Consider the amount S (n) = one? ?? Logs (i). Give a simple task f (n) so that zeros are s (n) o (f (n)). Explain

(Sigma starts with = 1 and ends at n)

How can I do this? Please explain step by step.

Just because log is monotonic: sum [i = 1..n] log (i)

then it o (n * log (n))

and to confirm that We can not improve this compulsion:

amount [i = 1..n] log (i) & gt; = Yoga [i = n / 2..n] log (i) & gt; = Sum [i = n / 2..n] log (n / 2) = (n / 2) * log (n / 2)

then it is omega * Log (n))

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