What are the steps to get a Central difference approximation in a Taylor series expansion with the steps i+-2 in x-direction?

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I see the result of a Central difference approximation in a Taylor series expansion with the steps $i\pm 2$ in $x$-direction, but what are the exact steps to get there? How do I get this result: Equation?

I know how to get to a central difference approximation with the steps $i\pm 1$. but the steps $i\pm 2$ I don't know about. please help me with this, thanks.