How to divide by infinite series?

Suppose you face the following problem:

You have to give scholarships to 10 students and to determine which students will get the scholarship, you have the following rating system:

Published a scientific paper - 2 points

Participated as an active speaker on a conference - 1 point

Volounteer - 0.5 points

Participated in a state competition in his/her field of study - 3 points

Participated in an international competition in his/her field of study - 5 points

The number of collected points + GPA = the total number of the student's points. Ten students who collected the most points will get the scholarship. The maximum number of points is 16.5.

However, now you face another problem: some studies don't have state or international competitions. Therefore, it is possible that the students of those studies would be discriminated against as they have a smaller chance of getting this scholarship. To solve this problem you could calculate the number of points each student collected and divide it with the maximum number of point he/she could have collected - 16.5 for studies in which there is a state/international competition and 8.5 for studies in which there is no state/international competition.

But how would you solve this problem if students can go to more than 1 competition, publish more than one scientific paper and participate in more than one conference? The maximum number of points that a student can collect is actually infinite and to solve the problem as mentioned above you would actually have to divide by infinite series. How would you go on in solving this problem?

• Choose the prettiest ones... Dec 7, 2016 at 18:30
• @DonAntonio papers or students ???
– user312097
Dec 7, 2016 at 18:33
• @A---B Students, of course. Who cares about the papers? :D) Dec 7, 2016 at 18:35
• Please I really need help with this question. Dec 8, 2016 at 10:43