`( 1-1/3 )(1-1/6)(1-1/15)...(1-1/253) < 2/5`
`=2/3×5/6×...×252/253`
`=4/6×10/12×...⋅504/506`
`=(1×4)/(2×3)×(2×5)/(3×4)×...×(21×24)/(22×23)`
`=(1×2×3×4^2×5^2⋅...⋅21^2×22×23×24)/2×3^2×4^2×...×22^2×23`
`=(1×24)/(3×22)`
`=24/66<2/5`
`⇒(1−1/3)(1−1/6)(1−1/15)...(1−1/253)<2/5`