Q. 23 - Calculus

Question

Evaluate the sums in Exercises $23–28$.

$\sum _{j=1}^3\sum _{k=1}^2{j}^k$ 

Step-by-Step Solution

Answer

The value of summation is $20$

Step 1. Given information

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

Step 2. Evaluating Summation

First separate the terms then simplify,

$$\begin{gathered} \sum _{j=1}^3\sum _{k=1}^2{j}^k=\sum _{j=1}^3\left(\sum _{k=1}^2{j}^k\right) \\ \sum _{k=1}^2{j}^k=j^k+j^2 \\ \Rightarrow \left(1^1+1^2\right)+\left(2^1+2^2\right)+\left(3^1+3^2\right) \\ =1+1+2+4+3+9 \\ =20 \end{gathered}$$