Convergence of Sequence $a_n=1+\frac{1}{4}+\frac{1}{7}+\ldots+\frac{1}{3n-2}$ Apply Cauchy's principle of convergence to prove that the sequence $\langle a_n\rangle$ defined by $$a_n=1+\frac{1}{4}+\frac{1}{7}+\ldots+\frac{1}{3n-2}$$ is not convergent
My attempt :
consider, 
\begin{align*}
 |a_{2m}-a_{m}|&=|1+1/4+1/7+\ldots+\frac{1}{3m-2}+\frac{1}{3m+1}+\ldots+\frac{1}{6m-2}\\
&-(1+1/4+1/7+\ldots+\frac{1}{3m-2})| \\ 
 &=|\frac{1}{3m+1}+\ldots+\frac{1}{6m-2}|\end{align*}
What do i do next ? i get confused after this step

for $m>1$$$|\frac{1}{3m+1}+\dots+\frac{1}{6m-2}| > m\times\frac{1}{6m-2} \nrightarrow 0 $$
