I'm studying for a calculus test I have later today and I'm having lots of trouble with these examples. Help with any or all of these is greatly appreciated.

1. Show that the SUMMATION from k=1 to infinity of ln[(k+1)/k)] diverges although ln[(k+1)/k] --> 0.

2. Determine whether the series converges or diverges: SUMMATION of 1/(1+2+...+k)

3. Determine whether the series converges or diverges: SUMMATION of ln(k)/e^k

4. Determine whether the series converges or diverges: SUMMATION of [k^(k/2)]/k!