Chapter 4 - Integration - 4.4 The Definition Of Area As A Limit; Sigma Notation - Exercises Set 4.4 - Page 297: 1

See explanation.

Using the rules of series: (a) $\frac{1}{8}+\frac{1}{6}+\frac{1}{4}+\frac{1}{2}=\sum_{k=1}^{4} \frac{1}{2 k}=\sum_{j=0}^{3} \frac{1}{2(j+1)}$ $(b)$ $10^{5}+10^{4}+10^{3}+10^{2}+10=\sum_{n=1}^{5}=10^{n}$