I feel a bit silly for asking this, but here goes...
I have the expression:
$$(1 - (1 - n^{c+d-1})^{n^{2d}})^{n^{2-2d}}$$
We can assume $d$ is a constant somewhere in the range $[0, \frac{1}{3}]$. Given $d$, I want to set $c$ to its minimum possible value such that the above expression does not vanish as $n$ goes to infinity (that is, it should not be $o(1)$ with respect to $n$). The parameter $c$ should be a function of $d$, but not a function of $n$.
Wolfram times out on this computation. What algebraic tricks can I use to simplify things and come up with an answer?