A Time Complexity Question

What is the time complexity of following function fun()? Assume that log(x) returns log value in base 2.

C

void fun()
{
    int i, j;
    for (i = 1; i <= n; i++)
        for (j = 1; j <= log(i); j++)
            printf("GeeksforGeeks");
}

Time Complexity of the above function can be written as ?(log 1) + ?(log 2) + ?(log 3) + . . . . + ?(log n) which is ? (log n!)
Order of growth of ‘log n!’ and ‘n log n’ is same for large values of n, i.e., ? (log n!) = ?(n log n). So time complexity of fun() is ?(n log n).
The expression ?(log n!) = ?(n log n) can be easily derived from following Stirling’s approximation (or Stirling’s formula).

log n! = n*log n - n = O(n*log(n))

Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.
Sources:
http://en.wikipedia.org/wiki/Stirling%27s_approximation

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My Personal Notes

C

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