Each term in the series can be represented by $5+9n,\,0\le n\le240$. In order for a term to be divisible by $5$, $n$ must be divisible by $5$. Hence...
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...