I can't seem to get this to sum, I'd be very thankful if someone could help me out.
$$\ 1, 1+\frac{1}{2},1+\frac{1}{2}+\frac{1}{3}, 1+\frac{1}{2} +\frac{1}{3}+ \frac{1}{4}\ldots$$
NOTE It would be nice if someone would post a consistent 'algorithm' / method that always works for sequences of this form that can be summed. As I find them very interesting and they've come up a lot for me lately....