Question

7. Use the Alternating Series Test to determine the convergence or divergence of the series

7. Use the Alternating Series Test to determine the convergence or divergence of the series 

a) \(\sum_{n=1}^{\infty} \frac{(-1)^{n} \sqrt{n}}{2 n+1}\)

b) \(\sum_{n=1}^{\infty} \frac{(-1)^{n} n}{2 n-1}\)


8. Use the Ratio Test or the Root Test to determine the convergence or divergence of the series

a) \(\sum_{n=0}^{\infty}\left(\frac{4 n-1}{5 n+7}\right)^{n}\)

b) \(\sum_{n=0}^{\infty} \frac{\pi^{n}}{n !}\)

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