Step 1 :The given series is \(\frac{1}{2(1)}+\frac{1}{2(2)}+\frac{1}{2(3)}+\cdots+\frac{1}{2(7)}\)
Step 2 :The series is a sum of fractions where the numerator is always 1 and the denominator is twice the index of the term in the series.
Step 3 :The series starts from the index 1 and ends at the index 7.
Step 4 :Therefore, the series can be represented using the summation notation as the sum of \(\frac{1}{2i}\) from i=1 to i=7.
Step 5 :Final Answer: The summation that represents the sum is \(\boxed{\sum_{i=1}^{7} \frac{1}{2 i}}\)