Hey there!

I'm really stuck on a question and i can't figure out how I should solve it.

I have a sum given by

$\displaystyle H_N = \sum_{i=1}^N\frac{1}{i}$

Given the special case where

$\displaystyle N = 2^{m+1} $

I have to prove that $\displaystyle H_N$ is logarithmically bounded by

$\displaystyle 1+\frac{\lg{N}}{2} \leq H_{N} \leq 1+\lg{N} $

And here's a *HINT* : Look at the terms

$\displaystyle \frac{1}{2^m+1}+...+\frac{1}{2^{m+1}}$

in $\displaystyle H_N$

Well, I really don't get it...if someone could help me I would greatly appreciate!

ps. I'm glad I found thoses forums, I'll certainly become an active member, being a studient in computer sciences :P.

THANKS!