6).  Use the Root Test to determine whether  ∞ n = 1 an  converges, where  an  is as follows. an =  n − 1 3n + 4     n   Evaluate the following limit.   lim  n → ∞  n |an|

Please use the theorem  to justify your answeer. Thanks

I need solution :Q7

Use the ratio test to determine whether diverges. an+1 lim n→∞0 an (a) Find the ratio of successive terms. Write your answer as a fully simplified fraction. For n ≥ 17, = lim lim n→∞⁰ an n=17 n→∞0 n² +8 8n converges or (b) Evaluate the limit in the previous part. Enter ∞ as infinity and -∞o as -infinity. If the limit does not exist, enter DNE. an+1 (c) By the ratio test, does the series converge, diverge, or is the test inconclusive? Choose