Question

test the series for convergence or divergence \[\sum_{1}^{\infty}\left( 2n +1 \right)^{n}\div \left( n ^{2n} \right)\]

Answer 1

converges i think

Answer 2

Use the root test:\[\sqrt[n]{\frac{(2n+1)^n}{n^{2n}}} = \frac{2n+1}{n^2} \to 0.\]Because the number is less than 1, the series converges.