Chapter 9.3, Problem 42E

EXPLORING CONCEPTS

Using a Function Let f be a positive, continuous. and decreasing function for $x\ge 1$, such that $a_n=f(n)$. Use a graph to rank the following quantities in decreasing order. Explain your reasoning.

(a) ${\displaystyle \underset{n=2}{\overset{7}{\sum }}{a}_n}$

(b) ${\displaystyle {\int }_1^{7}f(x)dx}$

(c) ${\displaystyle \underset{n=1}{\overset{6}{\sum }}{a}_n}$