यदि `""^(2n+1)P_(n-1):""^(2n-1)P_(n)=3:5`, तब `n` का मान ज्ञात कीजिए।

Explanation

प्रश्नानुसार, `(""^(2n+1)P_(n-1))/(""^(2n-1)P_(n))=3/5`
`rArr ((2n+1)!)/((n+2)!)xx((n-1)!)/((2n-1)!) = 3/5`
`rArr ((2n+1)(2n)(2n-1))/((n+2)(n+1)n(n-1)!) xx((n-1)!)/((2n-1)!) =3/5`
`rArr (2(2n+1))/((n+2)(n+1))=3/5`
`rArr 10(2n+1)=3(n+2)(n+1)`
`rArr 3n^(2) + 9n+ 6 = 20n+10`
`rArr 3n^(2)-11n-4=0`
`rArr (n-4)(3n+1) = 0`
`n = 4`