Answer: Choice A
Explanation:
Notice how the numerators (2,4,6,8) are multiples of 2. So we can say that they are of the form 2k, where k is a whole number from 1 to 4.
If k = 1, then 2k = 2*1 = 2
If k = 2, then 2k = 2*2 = 4
and so on until we reach k = 4 and 2k = 8.
Similarly, the denominators are also multiples of 2. We shift things 1 spot to the right. So we start with 4 instead of 2. So we need to add on 2
If k = 1, then 2k+2 = 2*1+2 = 4
If k = 2, then 2k+2 = 2*2+2 = 6
and so on.
[tex]\displaystyle \sum_{k=1}^{4}\frac{2k}{2k+2} = \frac{2}{4}+\frac{4}{6}+\frac{6}{8}+\frac{8}{10}[/tex]
