Expanding Summation notation
Write out each sum.
(\mathbf{a})\,\sum_{k=1}^{n}{\frac{1}{k}}\qquad\qquad\qquad\qquad(\mathbf{b})\,\sum_{k=1}^{n}k!(a) \sum_{k=1}^{n}{\frac{1}{k}}=1+{\frac{1}{2}}+{\frac{1}{3}}+\ \cdot\cdot\cdot\ +{\frac{1}{n}} (b) \sum_{k=1}^{n}k!\,=\,1!\,+\,2!\,+\,\cdot\,\cdot\,\cdot\,+\,n!