Question

In the following exercises, write each sum using summation notation.

$4-8+12-16+20-24$

Short answer

The summation notation is$\sum _{n=1}^6{\left(-1\right)}^{n+1}\left(4n\right)$.

Step-by-step solution

Step 1. Given information.

The given expression is,

$4-8+12-16+20-24$.

Step 2. Finding the summation notation.

Here, the number is multiple of $4$from $1$to $6$with alternative signs then we get,

$$\begin{gathered} 4-8+12-16+20-24 \\ n:1,2,3,4,5,6 \\ Terms:4,-8,12,-16,20,-24 \\ Pattern:{\left(-1\right)}^{1+1}\left(4.1\right),{\left(-1\right)}^{2+1}\left(4.2\right),{\left(-1\right)}^{3+1}\left(4.3\right),{\left(-1\right)}^{4+1}\left(4.4\right),{\left(-1\right)}^{5+1}\left(4.5\right),{\left(-1\right)}^{6+1}\left(4.6\right),....{\left(-1\right)}^{n+1}\left(4n\right) \end{gathered}$$

Then the sum can be written in the form of summation notation that is

$4-8+12-16+20-24=\sum _{n=1}^6{\left(-1\right)}^{n+1}\left(4n\right)$.