always converges as a summation to the formal power series designated by the same expression, and it often suffices to give a meaning to infinite sums and products, or other kinds of limits that one wishes to use to designate particular formal power series. It can however happen occasionally that one wishes to use a coarser topology, so that certain expressions become convergent that would otherwise diverge. This applies in particular when the base ring already comes with a topology other than the discrete one, for instance if it is also a ring of formal power series.
always converges as a summation to the formal power series designated by the same expression and it often suffices to give a meaning to infinite sums and products or other kinds of limits that one wishes to use to designate particular formal power series it can however happen occasionally that one wishes to use a coarser topology so that certain expressions become convergent that would otherwise diverge this applies in particular when the base ring already comes with a topology other than the discrete one for instance if it is also a ring of formal power series