use-the-root-test-to-determine-whether-the-series-n1nn23n2-displaystylesumn1inft

Question

Use the Root Test to determine whether the series ∑n=1∞(nn+2)3n2 \displaystyle \sum_{n=1}^{\infty} \left( \frac{n}{n+2} \$$right)^{3n^2}$$  converges absolutely or diverges.

Accepted Answer

The series converges absolutely

Answer

The series diverges

Answer

The test is inconclusive

Use the Root Test to determine whether the series ∑n=1∞(nn+2)3n2 \(\displaystyle\) \(\sum\)_{n=1}^{\(\infty\)} \(\left\)( \(\frac{n}{n+2}\) \(\right\))^{3n^2} converges absolutely or diverges.

Use the Root Test to determine whether the series $\sum_{n = 1}^{\infty} {(\frac{n}{n + 2})}^{3 n^{2}}$ converges absolutely or diverges.