=( 1/2- 1/3)+( 1/3- 1/4)+( 1/4- 1/5)+( 1/5- 1/6)+ +( 1/99- 1/ 100)
= 1/2+(- 1/3+ 1/3)+(- 1/4+ 1/4)+(- 1/5+ 1/5)+(- 1/6+ + 1/99)- 1/ 100
= 1/2+0+0+0+ +0- 1/ 100
= 1/2- 1/ 100
=49/ 100
1/2×3 is 1/2- 1/3.
(- 1/3+ 1/3)+(- 1/4+ 1/4)+(- 1/5+ 1/5)+(-65438+
This is called the cancellation of the split period.
Please adopt it if it helps.