`( 1 - 1/3 ) × ( 1 - 1/6 ) × ( 1 - 1/10 ) × ( 1 - 1/15 ) × ... × ( 1 - 1/780 ) × a = 1`
`2/3 × 5/6 × 9/10 × 14/15 × ... × 779/780 × a = 1`
`4/6 × 10/12 × 18/20 × 28/30 × ... × 1558/1560 × a = 1`
`{4 × 1}/{2 × 3} × {5 × 2}/{3 × 4} × {6 × 3}/{4 × 5} × {7 × 4}/{5 × 6} × .... × {41 × 38}/{39 × 40} × a = 1`
`{1 × 41}/{3 × 39} × a = 1`
`41/117 × a = 1`
`a = 1 : 41/117`
`a = 117/41`
`#dtkc`