Chapter 11.5, Problem 1E

To determine

To fill:The value of ${\displaystyle \sum _{i=1}^{n}i}$ .

Answer to Problem 1E

Thevalue of ${\displaystyle \sum _{i=1}^{n}i}$ is $\frac{n\left(n+1\right)}{2}$ .

Explanation of Solution

Given information:The summation notation is ${\displaystyle \sum _{i=1}^{n}i}$ .

The symbol of summation is used to represent the terms of a series in a particular manner.

The value of ${\displaystyle \sum _{i=1}^{n}i}$ is:

  $\begin{array}{c}{\displaystyle \sum _{i=1}^{n}i}=1+2+3+\cdots +n\\ =\frac{n\left(n+1\right)}{2}\end{array}$

Therefore, the value of ${\displaystyle \sum _{i=1}^{n}i}$ is $\frac{n\left(n+1\right)}{2}$ .