Question #7ea37

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Question #7ea37

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Answer 1 · 2017-03-30T00:03:20

$\frac{(2 n + 1)!}{(2 n - 1)!}$ $frac{(2n+1)!}{(2n-1)!}$

Expand the factorial in the numerator:

= $\frac{(2 n + 1) (2 n) (2 n - 1)!}{(2 n - 1)!}$ $frac{(2n+1)(2n)color(blue)((2n-1)!)}{color(blue)((2n-1)!)}$

$= (2 n + 1) (2 n)$ $=(2n+1)(2n)$

$= 2 (2 n + 1) (n)$ $=2(2n+1)(n)$

Answer 2 · 2017-03-30T00:08:23

$\frac{(2 n + 1)!}{(2 n - 1)!} = 4 n^{2} + 2 n$ $((2n+1)!)/((2n-1)!) = color(green)(4n^2+2n)$

Explanation:

$\frac{(2 n + 1)!}{(2 n - 1)!}$ $((2n+1)!)/((2n-1)!)$

$color(white)("XXX")=((2n+1) * (2n) * cancel((2n-1)) * cancel((2n-2)) * cancel((2n-3)) * ... * cancel(2) * cancel(1))/(cancel((2n-1)) * cancel((2n-2)) * cancel((2n-3)) * ... cancel(2) * cancel(1))$

$color(white)("XXX")=(2n+1) * (2n)$

$color(white)("XXX")=4n^2+2n$

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Question #7ea37

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