Q. 23 - Calculus

Question

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

$3+\frac{4}{8}+\frac{5}{27}+\frac{6}{64}+\frac{7}{125}$

Step-by-Step Solution

Answer

The sigma notation is $\sum _{k=1}^5\frac{k+2}{k^3}$

Step 1. Given Information

The given sum is $3+\frac{4}{8}+\frac{5}{27}+\frac{6}{64}+\frac{7}{125}$

Step 2. Explanation

The sum in sigma notation is written as, 

$$\begin{gathered} 3+\frac{4}{8}+\frac{5}{27}+\frac{6}{64}+\frac{7}{125}=\frac{1+2}{1^3}+\frac{2+2}{2^3}+\frac{3+2}{3^3}+\frac{4+2}{4^3}+\frac{5+2}{5^3} \\ =\sum _{k=1}^5\frac{k+2}{k^3} \\ Where, \\ m=1,n=5,a_k=\frac{k+2}{k^3} \end{gathered}$$