[JEE Advanced 1981] For every integer $n>1$, $(n!)^{1/n}<\frac{n+1}2$.
For every integer $n>1$, $(n!)^{1/n}<\frac{n+1}2$.
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✓ Vidaara Team
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· 1mo ago
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Answer: True.
By AM–GM, $(n!)^{1/n}<\frac{1+2+\cdots+n}n=\frac{n+1}2$ (strict for $n>1$).
JEE Advanced 1981 · Quadratic Equations and Inequations — verified solution by the Vidaara Team.
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