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What is the largest integer less than log_2(2/1) + log_2(3/2) + ... + log_2(64/63)?

May 9, 2022

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$$\log_2 \left(\dfrac{2}1\right) + \log_2\left(\dfrac32\right)+\cdots + \log_2 \left(\dfrac{64}{63}\right) \\ = \log_2 \left(\dfrac21 \times \dfrac32 \times \cdots \times \dfrac{64}{63}\right)\\ = \log_2 64\\ = 6$$

The answer is obvious at this point.

May 9, 2022