qqp question1: Is [math]\displaystyle\sum_{n=1}^{\infty} 2 \sin\left(\frac{2}{n}\right) [/math] convergent or divergent? question2: Why does the infinite sum [math]\displaystyle\sum_{n=2}^{\infty}(-1)^n\dfrac{1}{\ln(n!)}[/math] converge?