How does $\left( 1 - \left(1- \frac{1}{2^{2^k}}\right)\right)$ become $\left(1+ \frac{1}{2^{2^k}}\right)$?

I distributed the former but got negative $-\frac{1}{2^{2^k}}$. So it does not match the latter.

I'm basing the math from this website: http://zimmer.csufresno.edu/~larryc/proofs/proofs.mathinduction.html Please observe the math 2nd part of inductive step for the 2nd example(a recurrence formula)