Q. 22 - Calculus

Question

Write each of the sums in Exercises 21–28 in sigma notation. Identify $m,n,a_k$ in each problem.

$\frac{4}{3}+\frac{5}{4}+\frac{6}{5}+\frac{7}{6}+\frac{8}{7}+\frac{9}{8}+\frac{10}{9}+\frac{11}{10}$

Step-by-Step Solution

Answer

The sigma notation is  $\sum _{k=3}^{10}\frac{k+1}{k} \mathrm{and} m=3,n=10,a_k=\frac{k+1}{k}$

Step 1. Given Information

The given sum is  $\frac{4}{3}+\frac{5}{4}+\frac{6}{5}+\frac{7}{6}+\frac{8}{7}+\frac{9}{8}+\frac{10}{9}+\frac{11}{10}$

Step 2. Explanation

The sum in sigma notation is written as,

$$\begin{gathered} \frac{4}{3}+\frac{5}{4}+\frac{6}{5}+\frac{7}{6}+\frac{8}{7}+\frac{9}{8}+\frac{10}{9}+\frac{11}{10}=\frac{3+1}{3}+\frac{4+1}{4}+\frac{5+1}{5}+\frac{6+1}{6}+\frac{7+1}{7}+\frac{8+1}{8}+\frac{9+1}{9}+\frac{10+1}{10} \\ =\sum _{k=3}^{10}\frac{k+1}{k} \\ where, \\ m=3,n=10,a_k=\frac{k+1}{k} \end{gathered}$$