Question 995916
synthetic division
1/1+2+3+4+5...
 =1+1
===3 +3
======
=====6 +4
The first four terms are
x^99+3x^98+6x^97+10x^96+...
The coefficient of each term is the sum of all the preceding terms plus the coefficient of the next term.
The pattern will be 15,21,28,36.45.55.....
The coefficient of the 100th term is the sum of the preceding 99 terms plus the coefficient of the 100th term (100), so the quotient will be dividing x-1 into 4950x+100x or 5050 x.
That will go in 5050 times, and  we subtract  5050x-5050, so that the remainder is 5050.