For each of the following, determine whether the Ratio Test is inconclusive (that is, fails to give a definite answer), conclusive (and implying convergence) or conclusive (and implying divergence).

For the series $\displaystyle \sum_{n=5}^\infty \frac{(-3)^{n-1}}{\sqrt{n}}$ , the Ratio Test is Select inconclusive (i.e. we know nothing) conclusive (convergent) conclusive (divergent) .

For the series $\displaystyle \sum_{n=6}^\infty \frac{n}{10^n}$, the Ratio Test is Select inconclusive (i.e. we know nothing) conclusive (convergent) conclusive (divergent) .

For the series $\displaystyle \sum_{n=5}^\infty \frac{5 \sqrt{n}}{1+n^2}$, the Ratio Test is Select inconclusive (i.e. we know nothing) conclusive (convergent) conclusive (divergent) .

For the series $\displaystyle \sum_{n=3}^\infty \frac{7}{n^{4}}$, the Ratio Test is Select inconclusive (i.e. we know nothing) conclusive (convergent) conclusive (divergent) .