# How can the choice of coarsening factor affect Multigrid's convergence?

The linear system $$Ax=b$$ is coming from the discretization of an elliptic PDE. Multigrid method is used in order to solve it. Suppose $$c_0$$ is the coarsening factor on level 0 and $$c_m$$ the coarsening factor on level > 0. $$c_m$$ is choosed to be 2 (standard coarsening) in all levels > 0. How can the choice of $$c_0$$ can affect Multigrid's convergence? I assume that an aggressive coarsening at the beginning may increase the number of MG iterations while reducing the convergence time. Is there any possibility the choice of $$c_0$$ to lead MG to diverge?