19.(14分)(2011•浙江)已知公差不为0的等差数列$\{a_n\}$的首项$a_1$($a_1\in\mathbb{R}$),且$\frac{1}{a_1}$,$\frac{1}{a_2}$,$\frac{1}{a_4}$成等比数列.
(Ⅰ)求数列$\{a_n\}$的通项公式;
(Ⅱ)对$n\in\mathbb{N}^*$,试比较$\frac{1}{a_2}+\frac{1}{a_{2^2}}+\frac{1}{a_{2^3}}+\cdots+\frac{1}{a_{2^n}}$与$\frac{1}{a_1}$的大小.
参考答案
(Ⅰ)$a_n=na_1$;(Ⅱ)当$a_1>0$时,$T_n<\frac{1}{a_1}$;当$a_1<0$时,$T_n>\frac{1}{a_1}$