The geometric series equals if and only if .
By squinting at the notation, we can notice (not prove) a “well-known” matrix identity. (I keep forgetting it, so it’s not well-known to me).
If we let and make the following replacements:
(where is some matrix and is the identity matrix), we can get the following “identity”:
Now we interpret “1 over something” as its multiplicative inverse, so the right hand side becomes .
Therefore, by our “identity”,
which is actually true.