Number systems

you can get the sum by multiplying the average of numbers by the number of elements

sum=average of numbers * number of elements

we have 11 elements 100 to 110===> (110-100+1=11)
if we have a consecutive odd number of elements then the average is the middle number which 105

so sum is the product of 1/105 time 11
so, 11/105

manalq8, that approach only works for consecutive integers, because they are evenly spaced. Since the consecutive integers are in the denominator here, the terms are not evenly spaced (i.e. the difference between 1/100 and 1/101 is not the same as the difference between 1/101 and 1/102). As joeshmo pointed out, the averaging approach would not get us a precise answer for this problem.

To illustrate, let's look at a simpler set of fractions:

1/1 + 1/2 + 1/3 =

If we multiply the median by the number of terms, we'd say the total is 3/2. However, the actual total is 11/6, which is about 22% greater than the projected answer. Also, notice that in this case, the average of the first and last terms does not equal the median. (1/1 + 1/3)/2 = (4/3)/2=4/6 = 2/3 If we average all 3 terms, we get yet another result (11/18). You can try this with any set of fractions and you'll get similar results. The consecutive numebr tricks are great, but they only work if the actual terms in question are evenly spaced!

How would you actually solve this problem?
Manually add the numbers