Harmonic bounds

Algebra Level 5

α(n)=1+12+13+14+....+12n1\large{\alpha(n)=1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+....+\frac{1}{2^{n}-1}}

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

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

B)B)\quad α(100)>100\alpha(100) >100

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

D)D)\quad α(200)>100\alpha(200)>100

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