Can you write
$$1-x-\frac{x^2}{2!}+\frac{x^3}{3!}-\frac{x^4}{4!}+\frac{x^5}{5!}+\frac{x^6}{6!}-\frac{x^7}{7!}-\dots$$
with elementary functions, where the function is related to the Thue-Morse sequence stated here? I was told it converges with all inputs.
But I don't know how to write it in elementary functions. Thanks