On the whole, Divergent series are the work of the Devil and it's a Shame that one dares base any Demonstration on them. You can get whatever result you want when you use them, and they have given rise to so many Disasters and so many Paradoxes. Can anything more horrible be conceived than to have the following oozing out of you:
0 = 1 - 2n + 3n - 4n + etc.
where n is a whole Number? Risum teneatis amici. [Laughter retains friends]

Letter to Bernt Michael Holmboe (Jan. 1826) as quoted by Arild Stubhaug, Niels Henrik Abel and his Times: Called Too Soon by Flames Afar (2013)