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## 'Harmonically' printed from http://nrich.maths.org/

(a) Is it true that a large value of $n$ can be found such that:
$$S_n = 1 +{1\over 2} + {1\over 3} + {1\over 4} + ... + {1\over n}
> 100?$$

(b) By considering the area under the graph of $y = {1\over x}$
between $a ={1\over n}$ and $b = {1\over n-1}$ show that this
series grows like $\log n$.