Prove that for any integer

.

I am not sure where to start on this so maybe someone could give me a hint on what theorem(s) to use/where to start? thanks!

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- November 1st 2009, 12:17 PMnmatthies1Upper and Lower bound of the sequence log(n)
Prove that for any integer

.

I am not sure where to start on this so maybe someone could give me a hint on what theorem(s) to use/where to start? thanks! - November 1st 2009, 02:58 PMPlato
- November 1st 2009, 05:18 PMnmatthies1
I see how to observe

.

I don't quite see, however, how to observe that

is true. Could you elaborate? - November 2nd 2009, 04:40 AMKrizalid
Let be an antiderivative for thus

Now fix so that and then so now integrate for thus now the rest is just a matter of make-up, finally which is exactly what we wanted to prove.