Addendum to: On the rational approximation of the sum of the reciprocals of the Fermat numbers

As a corollary of the main result of our recent paper, {\em On the rational approximation of the sum of the reciprocals of the Fermat numbers} published in this same journal, we prove that for each integer $b\ge 2$ the irrationality exponent of ${\sum }_{n⩾0}{s}_2(n)\mathrm{/}{b}^n$ is equal to $2$.