Apply the Root Test to ∑n=1∞(3n4n+1)n\sum_{n=1}^{\infty} \left(\frac{3n}{4n+1}\right)^n∑n=1∞(4n+13n)n
L=34L = \frac{3}{4}L=43, so the series converges
L=1L = 1L=1, so the Root Test is inconclusive
L=0L = 0L=0, so the series converges absolutely
L=∞L = \inftyL=∞, so the series diverges