Question

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

$\frac{1}{4}+\frac{1}{9}+\frac{1}{16}+\frac{1}{25}+\frac{1}{36}+\frac{1}{49}+\frac{1}{64}$

Short answer

The sigma notation is$\sum _{k=2}^8\frac{1}{k^2}andm=2,n=8,a_k=\frac{1}{k^2}$

Step-by-step solution

Step 1. Given Information 

The given sum is$\frac{1}{4}+\frac{1}{9}+\frac{1}{16}+\frac{1}{25}+\frac{1}{36}+\frac{1}{49}+\frac{1}{64}$

Step 2. Explanation  

The sum in sigma notation is written as,

$$\begin{gathered} \frac{1}{4}+\frac{1}{9}+\frac{1}{16}+\frac{1}{25}+\frac{1}{36}+\frac{1}{49}+\frac{1}{64}=\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+\frac{1}{5^2}+\frac{1}{6^2}+\frac{1}{7^2}+\frac{1}{8^2} \\ =\sum _{k=2}^8\frac{1}{k^2} \\ where, \\ m=2,n=8,a_k=\frac{1}{k^2} \end{gathered}$$