Is log((n^2)!) , ?(?log?)? Please show steps of proof. (use limits if possible)
`Hey,
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By limit theorem
f(n)=w(g(n)) iff f(n)/g(n)=inf for n tending inf
f(n)=log(n^2!)
We can say that n^2!>=(n^2/2)^(n^2/2)=(n^2/2)^(n^2/2)
So,
f(n)=log(n^2!)>=log((n^2/2)^(n^2/2))=(n^2/2)*log(n^2/2)-------------------------eq1
g(n)=n*log(n)
So,
f(n)/g(n)=log(n^2!)/(n*log(n))
So, from equation 1
f(n)/g(n)>=(n^2)*log(n^2/2)/(2*n*log(n))=(n*log(n^2)-n*log(2))/(2*log(n))=(2*n*log(n)-n*log(2))/(2*log(n))
f/g>=n-n*log(2)/(2*log(n))
Since for n tending inf
f/g>=inf
which means f(n)/g(n)=inf
So, f(n)=w(g(n))
f(n)/g(n)=
Kindly revert for any queries
Thanks.
Is log((n^2)!) , ?(?log?)? Please show steps of proof. (use limits if possible)
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