IKMC 2027 - Grades 11-12 - Self-study SET 3 - Thematic Batch 3 Question 15

For integers n>1, $a_{n}$ =(3 n²−3 n+1)/(n²−n)³. Coprime positive integers p, q satisfy $a_{2}$+$a_{3}$+…+$a_{99}$=p/q. What is p−q?