As we can see on Wikipedia, there are some algebraic methods that give us finite sums for the Grandi's series
Let $S$ be the sum of the Grandi's series. Then
$1-S=S$ so that $S=1/2$
The algebraic manipulations above are not allowed because the Grandi's series doesn't converges.
Is there something similar related to the harmonic series? In other words, is there any "incorrect algebraic way" to get a finite sum for