(a) Is it true that a large value of $n$ can be found such that:

${\displaystyle S_n=1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{n}>100?}$

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