Since it's not terribly long, let's write the entire series out:
That's a sum of fractions. Every one of those fractions has a
numerator and a denominator.
Therefore we want to get this series in a short-hand form like this
We are told that the starting number of the index "i" is 1. So
let's put "1" in place of the words "starting integer"
Now let's make a list of all the values of the integer "i", the list
of all the numerators and the list of all the denominators:
i numerators denominators
1 1 3
2 2 4
3 3 5
4 4 6
5 5 7
6 6 8
7 7 9
8 8 10
9 9 11
10 10 12
11 11 13
12 12 14
13 13 15
14 14 16
15 15 17
16 16 18
17 17 19
18 18 20
Notice that there are 18 terms and therefore the ending integer for
the index "i" is 18. Therefore in place of the words "ending_integer",
we can put "18":
Look at the list of values for the index, that is, the "i"'s. Then look at
the list of numerators. Notice that they are all exactly the same as the
"i"'s. Therefore the numerators are all the same as i. Therefore we can put
"i" in place of the word "numerator" and we have this:
Now look at the list of denominators. Notice that every one of them is
2 more than the corresponding value in the list of index values "i" and
the numerators. So we see that each denominator is the value of both the
index "i" and the numerator with 2 added to it. Therefore we can put "i+2"
in place of the word "denominator". So the final answer is
Edwin
