12:02 PM
I suppose that at least some of these can be considered duplicates. The question is, which of them should be left open and which ones should be closed:
2

Show that $$\lim \frac{1}{n} \sum_{i=1}^n \frac{1}{i} =0$$ I've proved that this sequence converges (it is bounded and decreasing). NOW, I need to find a sequence that is bigger than this one and goes to zero. Maybe something using geometric serie of 1/2 Thanks in advance!

2

I can't seem to use certain methods such as $\varepsilon$-N, L'Hôspital's Rule, Riemann Sums, Integral Test and Divergence Test Contrapositive or Euler's Integral Representation to prove that $\lim_{n-> \infty} \frac{H_n}{n} = 0$ where $H_n$ is the nth Harmonic number $= \sum_{i=1}^{n} \frac{1}{... 3 How do I prove that$\dfrac{H_n}{n}$(where$H_n$is a harmonic number) converges to$0$, as$n \to \infty$? 5 Find the following limit: $$\lim_{n\to\infty} \left(1+\frac{1}{2}+...+\frac{1}{n}\right)\frac{1}{n}$$ My intuition says that this goes to zero, because$1/n\$ goes much faster to zero than the harmonic series go to infinity, but how can I prove this?

(I have answered one of them before looking for duplicates. Maybe I should have searched first - it is a kind of question which is very likely to have been asked before. On the other hand, the other answers probably did not look for them either.)

12:41 PM
One of the older posts only had two answers, so I voted to close it as a duplicate of today's post. (It has more answers.)
One of the posts seems mostly like the OP wants to ask about their own attempts.
I cannot decide between the remaining two posts. Having posted answer to one of them, I am probably not unbiased.