(1 - 1/4) x (1 - 1/9) x (1 - 1/16) x ... x (1 - 1/100)
= 3/4 . 8/9 . 15/16 . ... . 99/100
= (3 . 8 . 15 . ... . 99) / (4 . 9 . 16. ... . 100)
= [ (1 . 3) . (2 . 4) . (3 . 5) . ... . (9 . 11)] / [(2 . 2) . (3 . 3) (4 . 4) . ... . (10 . 10)]
= [(1 . 2 . 3 . ... . 9) . (3 . 4 . 5 . ... .11)] / [(2 . 3 . 4 . ... .10) . (2 . 3 . 4 . ... . 10)
= (1 . 2 . 3 . ... . 9) / (2 . 3 . 4 . ... .10) . (3 . 4 . 5 . ... .11) / (2 . 3 . 4 . ... .10)
= 1/10 . 11/2
= 11/20