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Prove that: ((2n)!)/(n !)={1. 3. 5 (2n-1...

Prove that: `((2n)!)/(n !)={1. 3. 5 (2n-1)}2^ndot`

Text Solution

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`L.H.S = ((2n)!)/(n!)`
`= (1.2.3.4.5.6..(2n-1).(2n))/(n!)`
`= ({2.4.6...(2n)}.{1.3.5....(2n-1)})/(n!)`
`= (2^(n){1.2.3...n}{1.3.5...(2n-1)})/(n!)`
`= 2^(n) {1.3.5..(2n-1)}`
`= R.H.S` Hence Proved.
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