for all .
First, I apologize if this is in the wrong section.
How do I go about demonstrating that the sum of log(i) from i up to n [eg. log(1) + log(2)... + log(n)] = O(n*logn)? That's Big-Oh notation. Any help/tips would be appreciated as I can't think where to start.
Thank you for your reply.
But it seems that I misunderstood. Are you able to conclude direcly from Black's proposition ?
Can you pass the equivalence to x-> infinity ? I have not done math for a long time but I remember it is not always such a basic thing to do.
Black has shown that
From this you get that
for , and with C=1, actually.
You really should look up the definition of Landau's Big-Oh notation, and preferably reproduce it without cheating on a white sheet of paper some time later. Definitions are very important in mathematics: without knowing them (or at the very least looking them up) you cannot hope to find the answer to an exercise like this.