Chapter 12.5, Problem 1E

To determine

To fill:The value of ${\displaystyle \sum _{i=1}^{n}c}$ such that $c$ is a constant.

Answer to Problem 1E

Thevalue of ${\displaystyle \sum _{i=1}^{n}c}$ is $cn$ such that $c$ is a constant.

Explanation of Solution

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

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

In the summation notation ${\displaystyle \sum _{i=1}^{n}c}$ , $n$ represents the number of terms. It can be written as:

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

Therefore, value of ${\displaystyle \sum _{i=1}^{n}c}$ is $cn$ such that $c$ is a constant.