Original formula = (1+2+3+…+10)+(11/kloc-0+…1/0).
Integer part1+2+3+…+10 =1x10/2 = 55.
Pay attention to the law of score:1/6 =1/2-1/3; 1/ 12= 1/3- 1/4… 1/90= 1/9- 1/ 10; 1/ 1 10= 1/ 10- 1/ 1 1
So the fractional part adds up = (1/2-1/3)+(1/3-1/4)+…+(110-/kloc-0).
= 1/2- 1/3+ 1/3- 1/4+...+ 1/9- 1/ 10+ 1/ 10- 1/ 1 1
Note that the middle part has been removed, so the decimal part =1/2-111= 9/22 has been added.
To sum up, the original formula is 55+9/22.