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## Homework Statement

[tex]\frac{1}{2^{k}+1} + \frac{1}{2^{k} +2} + ... + \frac{1}{2^k + 2^k} \geq \frac{1}{2}[/tex]

**2. The attempt at a solution**

Not too sure, I am working on a larger proof (not too much difficult) and the above is my attempt to prove the induction step k+1 (since [tex]\frac{1}{2^k + 2^k} = \frac{1}{2^{k+1}}[/tex]).

Should i try to factor out [tex]\frac{1}{2^k}[/tex]?