Chapter 11.4, Problem 8OE

To determine

To calculate:

Expanded form of ${\displaystyle \sum _{k=1}^4{k}^3}$ also read each symbol.

Answer to Problem 8OE

Expanded form of ${\displaystyle \sum _{k=1}^4{k}^3}$ is $100$ .

Explanation of Solution

Give information:

Expression:

  ${\displaystyle \sum _{k=1}^4{k}^3}$

Calculation:

It is given that,

  ${\displaystyle \sum _{k=1}^4{k}^3}$

So here symbol of given expression are:

  $4=$ Upper limit of summation.

  $k^3=$ Summand of the given expression.(containing first term and last term)

  $1=$ Lower limit of summation.

  $k=$ Index.

Given expression in expanded form is,

  $\begin{array}{l}{\displaystyle \sum _{k=1}^4{k}^3}=\\ ={\left(1\right)}^3+{\left(2\right)}^3+{\left(3\right)}^3+{\left(4\right)}^3\\ =\left(1\right)+\left(8\right)+\left(27\right)+\left(64\right)\\ =100\end{array}$

Therefore, expanded form of ${\displaystyle \sum _{k=1}^4{k}^3}$ is $100$ .