(1) Let {c, } be a sequence and 0 1 yet _n=] In is absolutely convergent

(1) Let{cn} be a sequence and O < r < 1. Then show that there exists a se- quence {11k} C N such that the series Ckxnk is absolutely convergent for all x E [r,r]. (2) Let xn # O for all n and L = lirnsup x +11 (a) Show that if L < 1 then xn is absolutely convergent. (b) Find {xn} such that L > 1 yet xn is absolutely convergent.