text 7 suppose that lim _n rightarrow infty sqrtn a_n geq 1 text test
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\text { (7) Suppose that } \lim _{n \rightarrow \infty} \sqrt{n} a_{n} \geq 1 \text { . Test the following series for convergence, } \sum_{n=1}^{\infty} \frac{a_{n}+\frac{1}{\sqrt{n}}}{n^{2} a_{n}^{2}}