Chapter 14.5, Problem 2AYU

To determine

To fill: ${\displaystyle \sum }_{k=1}^4\left(2k+1\right)=$__________.

Answer to Problem 2AYU

Solution:

24

Explanation of Solution

Given:

${\displaystyle \sum }_{k=1}^4\left(2k+1\right)$

Calculation:

$\underset{k=1}{\overset{4}{{{\displaystyle \sum }}^{\text{}}}}\left(2k+1\right)=\left(2\cdot 1+1\right)+\left(2\cdot 2+1\right)+\left(2\cdot 3+1\right)+\left(2\cdot 4+1\right)$

$=\left(2+1\right)+\left(4+1\right)+\left(6+1\right)+\left(8+1\right)$

$=3+5+7+9$

$=24$