I’ve always seen it explained as (100+0) + (99+1) + (98+2) + (97+3) + …

So you basically have 50 pairs of numbers that all equal 100. So 5000 right? But there is one number that doesnt have a pair to make 100. Which is 50. Obviously there arent two 50s to make 100. So its added by itself. 5050.

Its the same as the summation of 1 to 10. (0+10) + (1+9) + (2+8) + (3+7) + (4+6) + 5. Its 55.