Question

Evaluate the sums in Exercises 23–28.

$\sum _{j=1}^3\sum _{k=1}^2{k}^j$

Short answer

The value of summation is$17$

Step-by-step solution

Step 1. Given information

An expression is given as$\sum _{j=1}^3\sum _{k=1}^2{k}^j$

Step 2. Evaluating summation

First separate out the terms then simplify,

$$\begin{gathered} \sum _{j=1}^3\sum _{k=1}^2{k}^j=\sum _{j=1}^3\left(\sum _{k=1}^2{k}^j\right) \\ \sum _{k=1}^2{k}^j=1^j+2^j \\ \Rightarrow \left(1^1+2^1\right)+\left(1^2+2^2\right)+\left(1^3+2^3\right) \\ =1+2+1+4+1+8 \\ =17 \end{gathered}$$