[SOLVED] The difference of the harmonic series and 1/n comparsion

I recently had this classic example to determine if it converged or diverged
[MATH\frac{sin(n)}{n}][/tex]

I learned that you can use a comparison test using the squeeze theorem.



Then you would take the limit of

which was go to 0.

Because the function was greater than the original you can say the original converged as well to a limit of 0.

However, how would the harmonic series, diverge if you are basically determining the limit of the same thing

Edit: Poor question, trying to mark as solved, please disregard, if misused the concept of series and sequence

In...

http://www.mathhelpforum.com/math-he...eries-4-a.html

... it has been demonstrated that the series...

, (1)

... are both convergent and also their sum has been computed. I don't know if it exists an easier way to arrive at the same results... probably it exists (Itwasntme) ...

Kind regards

Thank you very much, it seems to me I am confusing the terms series and sequence perhaps, if there is a real difference