Apologies in advance if this is too easy of a question, but as an engineer, I am out of my depth. I am interested in the conditions under which the following expression approaches to $0$: $$1 - \left[1 - (1- e^{-a/b} )^c \right]^b~~~.$$ Specifically, if we hold $a$ constant and let $c\to\infty$, what are the necessary conditions on $b$ for this expression to approach $0$? If we hold $c$ constant and let $a\to\infty$, what are the necessary conditions on $b$ for this expression to approach $0$?
(if this is better suited for math.SE, my apologies again)
You just need the absolute value of the expression raised to the c power to be less than 1.