A quantity measuring the reflexivity of Banach spaces

For each $n$, we define $x_{n}(i)=1, i\leq n$ and $x_{n}(i)=-1,i>n$. Given any $(z_{n})_{n}\in \textrm{cbs}((x_{n})_{n})$, $z_{n}=\sum\limits_{i=k_{n-1}+1}^{k_{n}}\lambda_{i}x_{i}$. Then, for $n<m$, we get $$\sum\limits_{i=k_{n-1}+1}^{k_{n}}\lambda_{i}x_{i}(k_{m-1}+1)=-1, \quad \sum\limits_{i=k_{m-1}+1}^{k_{m}}\lambda_{i}x_{i}(k_{m-1}+1)=1.$$ This implies that $\|z_{n}-z_{m}\|=2$ and so $\textrm{ca}((z_{n})_{n})=2$. Thus, we obtain $R(c)=2$.