1. ## need help

floor function: the largest integer < x

Show:
1+ 2 + … + 2^(d-1) + 1 ≤ n if d = floor(log(base2)n)

2. Originally Posted by tukilala
floor function: the largest integer < x

Show:
1+ 2 + … + 2^(d-1) + 1 ≤ n if d = floor(log(base2)n)
$1+ 2 + … + 2^{d-1} = \sum_{k=0}^{d-1} 2^k = \frac{2^d-1}{2-1} = 2^d-1$
$1+ 2 + … + 2^{d-1}+1 = 2^d$