Challenge Level

(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 $\log n$.