Decide whether sequence or series is convergent or divergent

Question

Given:

A_n= 9n/(6n+5)

For both of the following answer blanks, decide whether the given sequence or series is convergent or divergent. If convergent, enter the limit (for a sequence) or the sum (for a series). If divergent, enter INF if it diverges to infinity, -INF if it diverges to minus infinity, or DIV otherwise.

(a) The series ∑(infinity), n=1 (A_n). = ? 

(b) The sequence {A_n} = ?

Answer 1

9n / (6n + 5) = 9 / (6 + 5/n)

(b). As n goes to infinity, 9 / (6 + 5/n) approaches 9/6 = 3/2. So the sequence converges to 3/2.

(a). Since the terms of the series do not approach 0, then by the nth term test for divergence, the series diverges.