Chapter 9, Problem 103RE

To determine

To find if the given statement or expression is true or false.

Answer to Problem 103RE

The statement is true as left hand side equals right hand side

Explanation of Solution

Given:

The statement:

  ${\displaystyle \sum _{k=1}^{8}3k}=3{\displaystyle \sum _{k=1}^{8}k}$

To find whether the following statement is true or false

  ${\displaystyle \sum _{k=1}^{8}3k}=3{\displaystyle \sum _{k=1}^{8}k}$

By properties of sums,

  ${\displaystyle \sum _{i=1}^{n}c{a}_i}=c{\displaystyle \sum _{i=1}^n{a}_i}$ , where c is a constant

Therefore, by properties of sums following statement is true

  ${\displaystyle \sum _{k=1}^{8}3k}=3{\displaystyle \sum _{k=1}^{8}k}$