Given,
[tex]\displaystyle \sf\Omega(n)=\sum_{k=2}^{n-1} \int_{0}^{\frac{\pi}{4}} \frac{\sin ^{2 k+1} x \cos ^{k} x+\sin ^{k} x \cos ^{2 k+1} x}{\sin ^{3 k+3} x+\cos ^{3 k+3} x} [/tex]
Then find,
[tex]\displaystyle \sf\lim _{n \rightarrow \infty} \frac{\Omega(n)}{n}[/tex]
[tex]\displaystyle \sf\Omega(n)=\sum_{k=2}^{n-1} \int_{0}^{\frac{\pi}{4}} \frac{\sin ^{2 k+1} x \cos ^{k} x+\sin ^{k} x \cos ^{2 k+1} x}{\sin ^{3 k+3} x+\cos ^{3 k+3} x} [/tex]
Then find,
[tex]\displaystyle \sf\lim _{n \rightarrow \infty} \frac{\Omega(n)}{n}[/tex]
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