MCQ
${n^n}{\left( {\frac{{n + 1}}{2}} \right)^{2n}}$ is
- ALess than ${\left( {\frac{{n + 1}}{2}} \right)^3}$
- BGreater than ${\left( {\frac{{n + 1}}{2}} \right)^3}$
- CGreater than ${(n!)^3}$
- ✓$(b)$ and $(c)$ both
Put $n = 2$, $y = {2^2}{\left( {\frac{3}{2}} \right)^4} = 4\,.\,\frac{{81}}{{8 \times 2}} = \frac{{81}}{4}\tilde - 20$
Option $(a) = {\left( {\frac{{n + 1}}{2}} \right)^3} = \frac{{27}}{8} < y$
Option $(b) = {\left( {\frac{{n + 1}}{2}} \right)^3} = \frac{{27}}{8} < y$
Option $(c) = {(2!)^3} = 8 < y$
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