# Homework Help: Inequality help

1. Oct 23, 2008

### Unassuming

1. The problem statement, all variables and given/known data

Show that

$$\frac{1}{2^k+1}+\frac{1}{2^k+2}+...+\frac{1}{2^{k+1}}>\frac{1}{2}$$

2. Relevant equations

3. The attempt at a solution

I cannot figure this out. It is part of a larger proof that I am trying to understand. Any help would be appreciated!

2. Oct 23, 2008

### dirk_mec1

Each of the terms $$\frac{1}{2^k+1},... \frac{1}{2^{k+1}-1}$$ is larger than $$\frac{1}{2^{k+1}}$$

There are 2*2^k - 2^k = 2^k terms so the whole sum is certainly larger than 1/2:

$$\frac{1}{2^k+1}+...+ \frac{1}{2^{k+1}} > \frac{2^k}{2^{k+1}} = \frac{1}{2}$$