qqp question1: Why does the infinite sum [math]\displaystyle\sum_{n=2}^{\infty}(-1)^n\dfrac{1}{\ln(n!)}[/math] converge? question2: Why does the series [math]\displaystyle\sum_{n=1}^{\infty}\dfrac{\sqrt{n+1}-\sqrt{n}}{n}[/math] converge?