Conceptually an integral corresponds to the area under a graph.
If that graph extends to infinity, the height of the graph must approach zero, since...
Erm... then I'm not quite sure what I can use or not.
Can you perhaps use the fact that a series $x_1 + x_2 + ...$ can only converge if $x_n \to 0$?...
Sometimes editing a thread title is an issue, but the issue is with vBulletin. If you ever want to change a thread title, and can't, just let me know...
Perhaps there are differences in terminology...I was taught that a function is concave up on an interval when its second derivative is positive, and...
Indeed. So we know that $H'(x)>0$ (positive not negative) for $0\le x \le 1$, but we still don't know anything about $H''(x)$.
We can only tell that...