Approximation for -1 exponent expression

[PhyPsy]

How do you come up with this approximation?

$[1+H(t-t_0)- \frac{1}{2}qH^2(t- t_0)^2]^{-1}\approx1+ H(t_0-t)+ \frac{1}{2}qH^2(t-t_0)^2+ H^2(t-t_0)^2$

Is there a rule that leads to this approximation?

 

[AlephZero]

Use the Binomial theorem.

1/(1 + x) = 1 - x + x^2 ...