In our Calc 1 class this is one of the proposed series:
$\displaystyle\sum\_{n\geqslant 1}\frac1{n}\prod\_{k=1}^n \left(1-\frac{\pi}{k}\right)$.
We have only been taught basic criteria, so no integration, just comparison test, quotient test, etc... Any way to tell this series diverges? (Because that is my intuition but I am unable to prove it)