Compute the value of summation

Question

Q. Compute the value of \(\frac{\psi}{18}\), where \(\psi = \frac{\sum_{\tiny\sigma=1}^{\tiny2024} \log_{\tiny\sqrt{6+\sqrt{6+\sqrt{6+...\infty}}}}^{{(3)}^{\int_{\tiny0}^{\tiny\sigma}dx}}}{25}\).

Answer : 

A. 4553

B. 4554

C. 5445

D. 2552