AMC 12 2025b Problem 7

What is the value of

$$\sum_{n=2}^{255} \frac{\log_2(1+\frac{1}{n})}{(\log_2 n)(\log_2(n+1))}$$

$\textbf{(A) } \dfrac{3}{4} \textbf{(B) } 1-\dfrac{1}{\log_2 255} \textbf{(C) } \dfrac{7}{8} \textbf{(D) } \dfrac{15}{16} \textbf{(E) } 1$