Let I ( n )=nn, J ( n )=1.3 .5 ldots . .(2 n -1) for all ( n 1), n ∈ N, then

Question

Let I ( n )=nn, J ( n )=1.3 .5 ldots . .(2 n -1) for all ( n >1), n ∈ N, then (A) I ( n )> J ( n ) (B) I(n)<J(n) (C) I(n)=J(n) (D) I ( n )=(1/2) J ( n )

Tardigrade Admin · Accepted Answer

AM ≥ GM (1+3+5+7+ ldots+(2 n-1)/n)>(J(n))(1/n), (n2/n)>(J(n))(1/n), nn>J(n), I(n)>J(n)

Q. Let $I (n) = n^{n}, J (n) = 1.3.5 \dots .. (2 n - 1)$ for all $(n > 1), n \in N$ , then

$I (n) > J (n)$

$I (n) < J (n)$

$I (n) = J (n)$

$I (n) = \frac{1}{2} J (n)$

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

Q. Let I(n)=nn,J(n)=1.3.5…..(2n−1) for all (n>1),n∈N, then

I(n)>J(n)

I(n)<J(n)

I(n)=J(n)

I(n)=21​J(n)