Compare to the series
[tex]\displaystyle\sum_{n=1}^\infty\frac7{10n}[/tex]
which is divergent. We have
[tex]\displaystyle\lim_{n\to\infty}\dfrac{\frac7{10n+3\sqrt n}}{\frac7{10n}}=\lim_{n\to\infty}\dfrac{10n}{10n+3\sqrt n}=1[/tex]
Because this limit is finite and positive, the original series must also be divergent (by the limit comparison test).
