Chapter 11.4, Problem 5OE

To determine

To explain:

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

Answer to Problem 5OE

Expanded form of ${\displaystyle \sum _{i=1}^{3}i}$ is $6$ .

Explanation of Solution

Give information:

Expression:

  ${\displaystyle \sum _{i=1}^{3}i}$

It is given that,

  ${\displaystyle \sum _{i=1}^{3}i}$

So here symbol of given expression are:

  $3=$ upper limit of summation.

  $i=$ Summand of the given expression.(containing first and last term)

  $1=$ Index or lower limit of summation.

Given expression in expanded form is,

  $\begin{array}{l}{\displaystyle \sum _{i=1}^{3}i}={\displaystyle \sum _{i=1}^3\left(1+2+3\right)}\\ =\left(1\right)+\left(2\right)+\left(3\right)\\ =6\end{array}$

Therefore, expanded form of ${\displaystyle \sum _{i=1}^{3}i}$ is $6$ .