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

Prove that: `(2n!)/(n!)=(2^n[1. 3. 5 (2n-1)])`

Text Solution

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Given
`frac{(2 n !)}{n !}=2^{n}(1.3 .5 ldots(2 n-1)) `
RHS `=(1.3 .5 ldots(2 {n}-1)) 2^{{n}}`
Multiply and divide by $2.4 .6 ldots .2 {n}$ on RHS
`{[1.3 .5 ldots(2 {n}-1)] 2^{{n}}=(1 cdot 3.5 ldots(2 {n}-1)) 2^{{n}} times frac{2 cdot 4 cdot 6 ldots 2 {n}}{2 cdot 4 cdot 6 ldots .2 {n}}} `
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