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How can $\sum_{n=1}^{\infty} 2^{-n} \frac{|x_n-z_n|}{1+|x_n-z_n|}$ be symmetric?

Problem:

Consider that the sequences are s.t. they obey:

$(x_n)$ follows $f(x)=x^3$

$(z_n)$ follows $f(x)=x^2$

Then the graph of this is unsymmetric.

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    $\begingroup$ It is symmetric in the sense that if your interchange the roles of $x_n$ and $y_n$, you get the same value. Not that $x_n = x_{-n}$. $\endgroup$ – kimchi lover Jan 11 at 21:31
  • $\begingroup$ @kimchilover Okay see, mixing the meaning of "symmetric". $\endgroup$ – mavavilj Jan 11 at 21:33

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