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

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

• 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 $x_n = x_{-n}$. – kimchi lover Jan 11 at 21:31
• @kimchilover Okay see, mixing the meaning of "symmetric". – mavavilj Jan 11 at 21:33