Step 1 :The problem is asking for the sum of a series. The series is defined by the formula \(\frac{2+i}{i}\) where \(i\) ranges from 1 to 4.
Step 2 :To solve this, we will iterate over the range 1 to 4, calculate the value of the formula for each \(i\), and sum up these values.
Step 3 :The sum of the series is calculated to be approximately 8.166666666666668.
Step 4 :Final Answer: The sum of the series is \(\boxed{8.166666666666668}\).