Final answer:
The series 9/4, 17/9, 25/14, 33/19, 41/24... converges to the value of 8/5.
Step-by-step explanation:
The series 9/4, 17/9, 25/14, 33/19, 41/24... is an example of a converging series. In this case, the series converges to a specific value. To find the value of convergence, we can analyze the pattern of the series. We notice that the numerator of each term follows the pattern of increasing by 8 each time, while the denominator follows the pattern of increasing by 5 each time. So, the terms can be represented by the formula:
Term n = (8n+1)/(5n-1)
As n approaches infinity, the value of Term n approaches 8/5. Therefore, the series converges to 8/5.