it is maybe at bit of a silly question, but one of our professors wrote the following equations and I would like to know what exactly he did. I'm sure it is something easy but I have no clue:
$$\frac{pc}{1+r} \approx \frac{c}{1+r+q}$$
Note: $p$ and $q$ are probabilities and $1-q = p$
My attempt is: $\dfrac{c}{1+r+q} = \dfrac{c}{1+r}\cdot \dfrac{1}{1+\dfrac{q}{1+r}} = \dfrac{c}{1+r}\cdot \left(1 - \dfrac{q}{1+r} + \left(\dfrac{q}{1+r}\right)^2 - \left(\dfrac{q}{1+r}\right)^3 + ....\right) \approx \dfrac{c}{1+r}\cdot \left(1 - q + q^2 - q^3 +...+ \right) \approx \dfrac{c}{1+r}\cdot \left(1 - q\right) = \dfrac{pc}{1+r}$