\text { Show that the function } T(x)=\sum_{n=2}^{\infty}\left(\frac{1}{x-n \pi}+\frac{1}{n \pi}\right) \text { is well-defined } \text { on }[0, \pi] \text {. That is, prove that the domain of the
function } T \text { contains the interval }[0, \pi] \text {. }