Recent content by shephard23

I've managed to work out that x(k+1) > ln(k) - ln(k+1) + 1/k > 0 from the inequality on the right. Does anyone have any suggestions on getting x(k+1) = 1 + 1/2 + ... + 1/k + 1/(k+1) > ln(k) - ln(k+1) + 1/k? I'm having the same trouble as before.

My apologies, when we use log in our course it means the natural log. Sorry, I've been using it for so long it just became second nature. log in the above problem is the natural log, ln.

Homework Statement Forgive my lack of LaTeX, not learned how to use it yet. Anyway, the problem is: Use the inequalities 1/(n+1) < ln(n+1) - ln(n) < 1/n to show that the sequence {xn} from n=1 to infinity defined by xn = 1 + 1/2 + ... + 1/n - ln(n) is strictly decreasing and bounded below...