1\1*3+1\3*5+1\5*7+.+1\95+99+1\97+99=?

1\1*3+1\3*5+1\5*7+.+1\95+99+1\97+99=?

Is it 1 / 1 * 3 + 1 / 3 * 5 + 1 / 5 * 7 +. + 1 / 95 * 97 + 1 / 97 * 99 =?
1/1*3=1/2*(1/1-1/3)
1/3*5=1/2*(1/3-1/5)
1/5*7=1/2*(1/5-1/7)
and so on
Original formula = 1 / 2 * (1-1 / 3 + 1 / 3-1 / 5 + 1 / 5 -... - 1 / 97 + 1 / 97-1 / 99)
All of them are in the middle
The result is 1 / 2 * (1-1 / 99) = 49 / 99