Use summation notation to write the series.
\[
\frac{1}{2(1)}+\frac{1}{2(2)}+\frac{1}{2(3)}+\cdots+\frac{1}{2(7)}
\]
Which summation represents the sum?
$\sum_{i=1}^{7} \frac{1}{i}$
$\sum_{i=1}^{7} \frac{1}{2 i}$
$\sum_{i=1}^{\infty} \frac{1}{2 i}$
$\sum_{i=1}^{\infty} \frac{1}{i}$
Answer
Final Answer: The summation that represents the sum is \(\boxed{\sum_{i=1}^{7} \frac{1}{2 i}}\)
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 \(\boxed{\sum_{i=1}^{7} \frac{1}{2 i}}\)
