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What is the solution to this equation: (2n+1)!/(2n-1)! =42 ;
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You want to solve,
`((2n+1)!)/((2n-1)!) = 42`
I can expand (2n+1)! as below.
`((2n+1)xx2nxx(2n-1)!)/((2n-1)!) = 42`
`(2n+1)xx2n = 42`
`(2n+1) xx n = 21`
`2n^2+n-21 = 0`
The solutions for above equation are,
`n = (-1+-sqrt(1+4xx2xx21))/(2xx2)`
`n = (-1+-sqrt(169))/4`
`n = (-1+-13)/4`
`n = 12/4 or n = -14/4`
We know `n!= -14/4` since factorial is not defined for negative numbers.
`n = 12/4 = 3`
The answer is 3.
Posted by thilina-g on June 7, 2012 at 6:51 PM (Answer #1)
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