# Harmonic bounds

Algebra Level 5

$\large{\alpha(n)=1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+....+\frac{1}{2^{n}-1}}$

For a positive integer $$n$$. define $$\alpha(n)$$ as above, then which of these are true?

$$A)\quad$$ $$\alpha(100)\leq 100$$

$$B)\quad$$ $$\alpha(100) >100$$

$$C)\quad$$ $$\alpha(200)\leq 100$$

$$D)\quad$$ $$\alpha(200)>100$$

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