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2025 AMC 12B Question 7

AMC12 · 2025 AMC 12B

Question 7

What is the value of

$$
\sum_{n=2}^{255} \frac{\log_2\left(1 + \frac{1}{n}\right)}{(\log_2 n)(\log_2(n+1))}?
$$
  1. $\dfrac{3}{4}$
  2. $1 - \dfrac{1}{\log_2 255}$
  3. $\dfrac{7}{8}$
  4. $\dfrac{15}{16}$
  5. $1$