Computing a sum of fractions using sigma notation Evaluate the following using sigma notation
$$\frac34 + \frac65 + \frac96 + \frac{12}{7} + \frac{15}{8}$$
For the denominator I get $\sum_{i=4}^8 i$ but how about the numerator? 

What about
$$\sum_{i=4}^8 \frac{3(i-3)}{i}=3\sum_{i=4}^81-9\sum_{i=4}^8\frac1i$$
