1 − 2 + 4 − 8 + ⋯

The series you provided is \( 1 - 2 + 4 - 8 + \ldots \). This can be expressed as an infinite series of the form: \[ S = 1 - 2 + 4 - 8 + 16 - 32 + \ldots \] This is a geometric series where the first term \( a = 1 \) and the common ratio \( r = -2 \).