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# Is this sequence $x_n=(1-\frac12)^{(\frac12-\frac13)^{…^{(\frac{1}{n}-\frac{1}{n+1})}}}$ uniformly distributed modulo 1?

The sequence $$(x_n) ,n=1,2,\cdots$$ is uniformly distributed mod 1 iff for real -valued continious function $$f$$ defined on the closed interval $$[0,1]$$ we have $$\lim_{N\to \infty} \frac1N \sum_{n=1}^{N} f(\{x_n\})=\int_{0}^{1} f(x) dx$$, Really am not able to apply that theorem for the following sequence $$x_n=(1-\frac12)^{(\frac12-\frac13)^{…^{(\frac{1}{n}-\frac{1}{n+1})}}}$$ to know if it is uniformly distributed or not ? However that theorem dosn’t need the convergence of a such sequence because the titled sequence converge according to the parity of $$n$$ which lie in $$[0,1]$$