How To Calculate the β with limit to infinity?
Rearranging the BJT forward active current gain:
$$I_c = βI_b $$
$$I_b = \frac{I_c}{β} $$
$$\lim_{β \to \infty} I_b = 0$$
Practically this means that for large β you can ignore the base current. In that case Ic = Ie, and you can find Ie using Ohm's law.