There are series and there are series.
Some series (Horatio Hornblower) follow one character over the years while other series are really a single over-sized novel (Zelazny's Amber chronicles).
And other series (Darkover) are just a framework for hosting different stories with different characters and themes.
Sure, some series are purely commercial "variations on a theme" that seek to retell the same story over and over with minor tweaks but it is a big leap to extrapolate from the specific to the general.
The case can be made that series are a narrative form all their own, as distinct from novels as novels are from short stories.