n^n left( frac{n+1}{2} right)^{2n} is | vedclass

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(D) Let $y = n^n \left( \frac{n+1}{2} ight)^{2n}$.For $n = 2$:$y = 2^2 \left( \frac{3}{2} ight)^4 = 4 	imes \frac{81}{16} = \frac{81}{4} = 20.25$

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$(b)$ and $(c)$ both

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(D) Let $y = n^n \left( \frac{n+1}{2} ight)^{2n}$.For $n = 2$:$y = 2^2 \left( \frac{3}{2} ight)^4 = 4 	imes \frac{81}{16} = \frac{81}{4} = 20.25$.Check Option $(a)$ and $(b)$:$\left( \frac{n+1}{2} ight)^3 = \left( \frac{3}{2} ight)^3 = \frac{27}{8} = 3.375$.Since $20.25 > 3.375$,$y$ is greater than $\left( \frac{n+1}{2} ight)^3$.Check Option $(c)$:$(n!)^3 = (2!)^3 = 2^3 = 8$.Since $20.25 > 8$,$y$ is greater than $(n!)^3$.Thus,both $(b)$ and $(c)$ are correct.

$n^n \left( \frac{n+1}{2} \right)^{2n}$ is

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