Investigate convergence of the following series:

$\sum _{n=0}^{\mathrm{\infty}}{\left(\frac{2+(-1{)}^{n}}{\pi}\right)}^{n}$

Which convergence criterion shoul be applied?

$\sum _{n=0}^{\mathrm{\infty}}{\left(\frac{2+(-1{)}^{n}}{\pi}\right)}^{n}$

Which convergence criterion shoul be applied?