Answer
5 ; convergent
Work Step by Step
Let's look at this as a rational function. We know from previous knowledge that the limit of a rational function is one of the following:
a) If the powers of top and bottom are equal, then the limit is equal to the coefficients of the highest powered terms on the top divided by the bottom and the sequence is convergent.
b) If the power on top is higher then the limit is infinity and the sequence is divergent
c) If the power on the bottom is higher then the limit is 0 and the sequence is convergent.
In this instance, it is case (a) and the top's coefficient is 5 and the bottom's is 1, so the limit converges to 5.
