Recent content by Deano10

I have had a further look at this and think that I can adapt the proof of the fact that the limiting difference between the harmonic series and natural logarithm tending to the Euler constant to prove one side of the inequality. However, this still leaves the other side of the inequality...

The picture I had in mind was of that of log (n) with step functions (of the values in the inequalities) both above and below the graph drawn out by log (n). It is this that leads me to think the proof must involve the use of bounding step functions, but I cannot see how to begin.

Homework Statement Prove that for any integer n >= 2, 1/2 + 1/3 + ... + 1/n <= log(n) <= 1 + 1/2 + 1/3 + ... + 1/(n-1) Homework Equations None The Attempt at a Solution I can see pictorally why the inequality holds true but despite numerous am struggling to make any real...

I don't know how I didn't see that before...thanks! How do I then go on to show that the integral of f(x) between c-delta and c+delta (and therefore the whole function between a and b) is greater than 0?

Apologies for bringing up an old thread but I am attempting to solve a similar problem... I can understand the workings of the proof that has been discussed above, but am having difficulties in actually writing it formally. In particular, I am having trouble trying to prove why if at some...