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How do I show $H_{2^k} \leq k + 1$ for each $k \geq 0$?

I don't know how to do this question so can anyone help me?

user110344
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    If you can say a little bit about what you know/have tried (even if it's not very much), you're likely to get a better response. Try at least giving us the definition of a harmonic number. – BaronVT Nov 21 '13 at 01:20
  • Please do not vandalize your questions. This renders them useless to others and is disrespectful to the efforts of those who have provided answers. – robjohn Nov 21 '13 at 19:03

1 Answers1

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Hint: You can prove it by induction. To get from $H_{2^k}$ to $H_{2^{k+1}}$, you add $2^k$ terms, each of which is $\lt \frac{1}{2^k}$.

André Nicolas
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