1. Tardigrade
  2. Question
  3. Mathematics
  4. Let I ( n )=nn, J ( n )=1.3 .5 ldots . .(2 n -1) for all ( n >1), n ∈ N, then

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Q. Let $I ( n )=n^{n}, J ( n )=1.3 .5 \ldots . .(2 n -1)$ for all $( n >1), n \in N$, then

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Solution:

$AM \geq GM$
$\frac{1+3+5+7+\ldots+(2 n-1)}{n}>(J(n))^{\frac{1}{n}}$,
$\frac{n^{2}}{n}>(J(n))^{\frac{1}{n}}$,
$n^{n}>J(n)$,
$I(n)>J(n)$