AMC 12 2025 Part B Problem 7

What is the value of

\sum_{n=2}^{255}\frac{\log_{2}\!\left(1+\frac{1}{n}\right)}{\left(\log_{2}n\right)\left(\log_{2}(n+1)\right)}\ ?

Answer Choices:

A. \dfrac{3}{4}

B. 1-\dfrac{1}{\log_{2}255}

C. \dfrac{7}{8}

D. \dfrac{15}{16}

E. 1