Chapter 12.1, Problem 47E

To determine

Calculate the sum of the equation.

Answer to Problem 47E

The sum of the equation is $34$ .

Explanation of Solution

Given:

It is given in the equation that the equation is ${\displaystyle \sum _{i=1}^{3}i{2}^i}$ .

Concept Used:

In this use the concept of, putting the number in the equation and expand it.

Calculation:

Here, the equation is ${\displaystyle \sum _{i=1}^{3}i{2}^i}$ .

Put each and every number in the equation of i ,

  $\begin{array}{l}{\displaystyle \sum _{i=1}^{3}i{2}^i}=(1)2^1+(2)2^2+(3)2^3\\ {\displaystyle \sum _{i=1}^{3}i{2}^i}=1(2)+2(4)+3(8)\\ {\displaystyle \sum _{i=1}^{3}i{2}^i}=2+8+24=34\end{array}$

Conclusion:

The sum is $34$ .