Determine the convergence of the series ∑n=1∞(an)\sum_{n=1}^{\infty} (a_n)∑n=1∞(an) where an+1=an⋅n2n+1a_{n+1} = a_n \cdot \frac{n}{2n+1}an+1=an⋅2n+1n and a1=1a_1 = 1a1=1.
Converges by Ratio Test
Diverges by Ratio Test
Converges by Root Test
Inconclusive