`P=(1-1/3).(1-1/6).(1-1/10) (14/15).....(1-1/780)`
`=2/3 . 5/6. 9/10 . ...740/741. 779/780 `
`= 4/6 . 10/12 . 18/20...... 1558/1560`
`=1.4 /2.3. 2.5/3.4. 3.6/4.5 ... 38.41 /39.40`
`=`$\dfrac{1.4.2.3.5.6}{2.3.3.4.4.5} .... 38.41/39.40$
`=` $\dfrac{(1.2.3 .... 38) (4.5.6...41)}{ (2.3.4...39) (3.4.5...40)}$
`= 1/39 . 41/3`
`= 41/117`