19.(1) 当

时,

······ 2分
又

适合上式
∴

···································································· 3分
由

·························································· 5分
(2)

···································································· 6分
∵

∴

,即

∴ {
cn}的最大项为

··································································· 9分
∴

∴

∴实数
m的取值范围为

················································ 12分