If a series such as '$a$' below adds to infinity:

$a = 1 + 2 + 4 + 8 + 16 + \cdots\to \infty$

Multiplying '$a$' by $2$ yields:

$2a = 2 + 4 + 8 + 16 + \cdots\to \infty$

However when I subtract these two series, I find a paradoxical answer. Series '$a$', which supposedly adds to infinity also equals -1.

$2a - a = (2 + 4 + 8 + 16 + \cdots) - (1 + 2 + 4 + 8 + 16 +\cdots)$

$2a - a = -1 + (2 - 2) + (4 - 4) + (8 - 8) + \cdots$

$a = -1 + 0 + 0 + 0 + 0 + \cdots$

$a = -1$

Does this mean that infinity equals $-1$?