Assume ${{T}}$ is an arbitrary $m\times m$ matrix, and ${{D}}$ is a diagonal matrix, by knowing the fact that ${{T}}^n {{D}}^n \neq({{T}} {{D}})^n$, is there any way to find a close form solution for the below series?
${{{I}}}+{{T}}^1 {{D}}^1+{{T}}^2 {{D}}^2+\cdots+{{T}}^{M-1} {{D}}^{M-1}$