# Prove the following by induction (or otherwise):

1. Aug 14, 2010

### seeker101

Does anyone have any suggestions on how to go about proving that

$$\left\lceil\frac{1}{2}{\lceil \log m\rceil}^2\right\rceil$$ is less than m-1, for m > 64? (using log to the base 2)

2. Aug 14, 2010

### CRGreathouse

Prove that it's true for 64 < m <= 128, then use induction to show that it's true for ranges that are 2, 4, 8, ... times as large.

3. Aug 15, 2010

### seeker101

Much appreciated!
Thank you.

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