Use the Root Test on ∑n=1∞(n+25n+1)n\sum_{n=1}^{\infty} \left(\frac{n+2}{5n+1}\right)^n∑n=1∞(5n+1n+2)n Compute L=limn→∞annL = \lim_{n \to \infty} \sqrt[n]{a_n}L=limn→∞nan and determine convergence.
L=15L = \frac{1}{5}L=51, converges
L=1L = 1L=1, inconclusive
L=25L = \frac{2}{5}L=52, converges
L=15L = \frac{1}{5}L=51, diverges