Let $(x_n)$ be a sequence in a Banach space $X$. We denote $${\rm coef}(X,(x_n))=\{a\in\Bbb R^\Bbb N:\sum_na(n)x_n\mbox{ converges}\}.$$ In this talk, we focus on Borel reducibility between equivalence relations of $\Bbb R^\Bbb N/{\rm coef}(X,(x_n))$. This kind of research begin from Dougherty and Hjorth's results on $\Bbb R^\Bbb N/\ell_p\,(p\ge 1)$ and $\Bbb R^\Bbb N/c_0$