Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer does not exist, enter DNE.)Part 1) an= (5n) /(1+9n)limn→[infinity] an =?Part 2) (1,1/2,1/2,1/3,1/3,1/4,1/4,1/5...)l imn→[infinity] an =?

The sequence converges to 5/9.

Step-by-step explanation:

Suppose we have a sequence

Limit test:

If L is a constant number, the sequence converges to L.

If L = 0, the test is inconclusive.

Otherwise, the sequence diverges.

In this question:

Test:

Infinity limit, we consider the term with the highest degree in the numerator and in the denominator.

The sequence converges to 5/9.