Long division of polynomial

Question

Using long division , please show the steps to go from 2/(2-x) to 1 + 1/2 X + 1/4 X^2 + ... (1/2 X) ^n-1

Answer 1

1 + x/2 + x²/4

2 - x | 2 + 0x + 0x² + 0x³ + 0x⁴

2 - x

x + 0x²

x - x²/2

x²/2 + 0x³

x²/2 - x³/8

That is how you start. The division never ends since the remainder is never zero.

I do not know what the "n - 1" means.