Chern Class of the Structure Sheaf of a Cartier Divisor

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I'm reading 3264 and all that page 486. They calculate the chern class of the structure sheaf of a Cartier divisor.

Let $Y\subseteq X$ be a Cartier divisor. Then we have short exact sequence: $$0\rightarrow \mathscr O_{X}(-Y)\rightarrow\mathscr O_{X}\rightarrow\mathscr O_Y\rightarrow 0$$

Hence $$c(\mathscr O_{Y}) = \frac{c(\mathscr O_X)}{c(\mathscr O_X(-Y))} = \frac{1}{1-[Y]}$$

I'm okay up to now. But then, they says: $$\frac{1}{1-[Y]} = 1+[Y]$$ which confuses me. Shouldn't it be $1+[Y]+[Y]^2+\dots+[Y]^n$? How to see $[Y]^2 = 0$? enter image description here