Apply the Root Test to ∑n=1∞(2n+35n−1)n\sum_{n=1}^{\infty} \left(\frac{2n+3}{5n-1}\right)^n∑n=1∞(5n−12n+3)n.
Converges by Root Test with limit 25\frac{2}{5}52
Diverges by Root Test with limit 25\frac{2}{5}52
Converges by Root Test with limit 31\frac{3}{1}13
The Root Test is inconclusive