Sendo $S=\frac{\pi }{2}+\frac{\pi }{3}+\frac{\pi }{4}+\frac{\pi }{9}+\frac{\pi }{8}+\frac{\pi }{27}+\cdots +\frac{\pi }{2^n}+\frac{\pi }{3^n}+\cdots$, o valor do $\cos (S-x)$ é igual a